measuring the cost of living
Consumer Price Index
How the CPI Is Calculated
Problems with the CPI
Contrasting the CPI and GDP Deflator
Correcting Variables for Inflation:
The two-factor theory of motivation (also known as Herzberg's motivation-hygiene theory or dual-factor theory) states that there are certain factors in the workplace that cause job satisfaction, while a separate set of factors cause dissatisfaction.
measuring the cost of living
Consumer Price Index
How the CPI Is Calculated
Problems with the CPI
Contrasting the CPI and GDP Deflator
Correcting Variables for Inflation:
The two-factor theory of motivation (also known as Herzberg's motivation-hygiene theory or dual-factor theory) states that there are certain factors in the workplace that cause job satisfaction, while a separate set of factors cause dissatisfaction.
The Customer Journey applied to the buying and shopping experience at IKEA: from the wow moment to the how moment.
Step by step as an example how to make the customer journey an interesting and useful tool.
Quantitative Analysis For Management 11th Edition Render Test BankRichmondere
Full download : http://alibabadownload.com/product/quantitative-analysis-for-management-11th-edition-render-test-bank/ Quantitative Analysis For Management 11th Edition Render Test Bank
McDonald’s is one of the largest chains of hamburger fast food restaurants in the world. Since its foundation in the year 1940, McDonald’s has successfully increased its prominence globally.
For more visit - https://myassignmenthelp.com/case-study/mcdonalds-pestle-analysis-marketing-case-study.html
The Customer Journey applied to the buying and shopping experience at IKEA: from the wow moment to the how moment.
Step by step as an example how to make the customer journey an interesting and useful tool.
Quantitative Analysis For Management 11th Edition Render Test BankRichmondere
Full download : http://alibabadownload.com/product/quantitative-analysis-for-management-11th-edition-render-test-bank/ Quantitative Analysis For Management 11th Edition Render Test Bank
McDonald’s is one of the largest chains of hamburger fast food restaurants in the world. Since its foundation in the year 1940, McDonald’s has successfully increased its prominence globally.
For more visit - https://myassignmenthelp.com/case-study/mcdonalds-pestle-analysis-marketing-case-study.html
1. (6 points) A soda company want to stimulate sales in this econo.docxSONU61709
1. (6 points) A soda company want to stimulate sales in this economic climate by giving
customers a chance to win a small prize for ever bottle of soda they buy. There is a 20%
chance that a customer will find a winning icon at the bottom of the cap upon opening up a
bottle of soda. The customer can then redeem that bottle cap for a small prize. Now, if yours
truly buys a 6-pack of soda, what is the probability that I will win something, i.e., at least
winning a single small prize?
2. (6 points) A department store manager has decided that dress code is necessary for team
coherence. Team members are required to wear either blue shirts or red shirts. There are 9
men and 6 women in the team. On a particular day, 4 men wore blue shirts and 5 other wore
red shirts, whereas 3 women wore blue shirts and 3 others wore red shirt. Apply the Addition
Rule to determine the probability of finding men or blue shirts in the team.
3. (6 points) A consulting company wants to estimate the proportion of Americans who own
their house. What sample size should be obtained if the estimate is expected to be within 0.04
with 95% confidence if
a. they use an estimate of 0.675 from the Census Bureau?
P=0.675
1-p=0.325
E=0.04
Sample size is 527
b. they do not use any prior estimates? But in solving this problem, you are actually using a
form of "prior" estimate in the formula used. In this case, what is your "actual" prior
Estimate? Please explain.
Actual estimate sis 0.675 which is the proportion of American who own their house.
4. (6 points) Most of us love peaches, but hate buying those that are picked too
early. Unfortunately, by waiting until the peaches are almost ripe to pick carries a risk of
having 30% of the picked rot upon arrival at the packing facility. If the packing process is all
done by machines without human inspection to pick out any rotten peaches, what would be
the probability of having at most 4 rotten peaches packed in a box of 12?
5. (6 points) There is a screening test for a rare disease that affects 1.5% of the population.
Unfortunately, the reliability of this screening test is only 70%. What it means is that it gives
a false positive result 30% of the time. Fortunately, there is no false negative. Suppose if
you are tested positive for this rare disease, what is the probability that you are actually
inflicted by this rare disease? (Hint: Bayes’ Theorem)
Percentage of population affected = 1.5%
Reliability = 70%
Percentage of false positive result = 30%
Note that there is no false negative.
Let A1, A2, ... , An be a set of mutually exclusive events that together form the sample space S.
Let B be any event from the same sample space, such that P(B) > 0. Then,
Plug in the given values:
6. (6 points) Assume that you toss a fair six-faced die two times.
(a) (2 pt) How many possible outcomes are in the sample space? Explain your answer.
First time number of outcome =6,
Second time number of outcome =6
Total outcome = 6*6 ...
1.value3.68 pointsExercise 5-91Nineteen percent of all .docxhyacinthshackley2629
1.
value:
3.68 points
Exercise 5-91
Nineteen percent of all liquid crystal displays (LCDs) are manufactured by Samsung. What is the probability that in a collection of three independent LCD purchases, at least one is a Samsung? (Round your answer to 3 decimal places.)
Probability
2.
value:
3.44 points
Exercise 5-13
A study of 200 advertising firms revealed their income after taxes:
Income after Taxes
Number of Firms
Under $1 million
103
$1 million to $20 million
52
$20 million or more
45
(a)
What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)
Probability
(b-1)
What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)
Probability
(b-2)
What rule of probability could be applied?
Rule of Probability
3.
value:
3.44 points
Exercise 5-68
An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketball games. The company president always invites one of the 7 vice presidents to attend games with him, and claims he selects the person to attend at random. One of the 7 vice presidents has not been invited to attend any of the last 3 Lakers home games.
What is the likelihood this could be due to chance? (Round your answer to 3 decimal places.)
Likelihood
3.44 points
Exercise 5-27
Refer to the following table.
First Event
Second Event
A1
A2
A3
Total
B1
4
2
6
12
B2
4
4
5
13
Total
8
6
11
25
(a)
Determine P(A1). (Round your answer to 2 decimal places.)
P(A1)
(b)
Determine P(B2|A2). (Round your answer to 2 decimal places.)
P(B2|A2)
(c)
Determine P(B2 and A3). (Round your answer to 2 decimal places.)
P(B2 and A3)
5.
value:
3.44 points
Exercise 5-26
All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .72, the probability the second truck is available is .51, and the probability that both trucks are available is .42:
What is the probability neither truck is available? (Round your answer to 2 decimal places.)
Probability
6.
value:
3.44 points
Exercise 5-90
The probability a HP network server is down is .065. If you have four independent servers, what is the probability that at least one of them is operational? (Round your answer to 6 decimal places.)
Probability
7.
value:
3.44 points
Exercise 5-64
There are 26 families living in the Willbrook Farms Development. Of these families 13 prepared their own federal income taxes for last year, 10 had their taxes prepared by a local professional, and the remaining 3 by H&R Block.
(a)
What is the probability of selecting a family that prepared their own taxes? (Round your answers to 3 decimal places.)
Probability
.
1) Let P(A) = 0.35, P(B) = 0.30, and P(A ∩ B) = 0.17.a.Are A.docxdorishigh
1) Let P(A) = 0.35, P(B) = 0.30, and P(A ∩ B) = 0.17.
a.
Are A and B independent events?
Yes because P(A | B) = P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
b.
Are A and B mutually exclusive events?
Yes because P(A | B) = P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
c.
What is the probability that neither A nor B takes place
2)
(Use computer) Assume that X is a Poisson random variable with μ = 40. Calculate the following probabilities. (Round your intermediate calculations and final answers to 4 decimal places.)
a.P(X ≤ 29)
b.P(X = 33)
c.P(X > 36)
d.P(36 ≤ X ≤ 47)
3)
Scores on the final in a statistics class are as follows.
61
23
62
50
64
68
66
80
76
48
72
78
46
58
56
52
74
53
70
54
Click here for the Excel Data File
a.
Calculate the 25th, 50th, and 75th percentiles. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
25th percentile
50th percentile
75th percentile
b-1.
Calculate the IQR, lower limit and upper limit to detect outliers. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)
IQR
Lower limit
Upper limit
b-2.
Are there any outliers?
Yes
No
4)
Consider the following observations from a population:
124
231
29
84
84
17
175
99
29
Click here for the Excel Data File
a.
Calculate the mean and median. (Round "mean" to 2 decimal places.)
Mean
Median
b.
Select the mode. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.)
84
29
99
17
124
231
175
5)
Consider the following sample data:
x
14
22
24
19
27
y
13
18
20
23
25
a.
Calculate the covariance between the variables. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Covariance
b-1.
Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Correlation coefficient
b-2.
Interpret the correlation coefficient.
There is relationship between x and y.
A a(a(42)) , perfect , weak, strong, or no
6)
The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 93% of the time; that is, there is a 0.93 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 1% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 90% of the drivers drive below the speed limit on this ...
STAT 200 Introduction to Statistics Final Examination, Spri.docxrafaelaj1
STAT 200: Introduction to Statistics
Final Examination, Spring 2019 OL3
Page 1 of 8
STAT 200
OL3 Sections
Final Exam
Spring 2019
The final exam will be posted at 12:01 am on April 19, 2019, and
it is due at 11:59 pm on April 21, 2019 Eastern Time.
This is an open-book exam. You may refer to your text and other course materials
for the current course as you work on the exam, and you may use a calculator,
applets, or Excel. You must complete the exam individually. Neither collaboration
nor consultation with others is allowed. It is a violation of the UMUC Academic
Dishonesty and Plagiarism policy to use unauthorized materials or work from
others.
Answer all 20 questions. Make sure your answers are as complete as possible,
particularly when it asks for you to show your work. Answers that come straight
from calculators, programs or software packages without any explanation will not
be accepted. If you need to use technology (for example, Excel, online or hand-
held calculators, statistical packages) to aid in your calculation, you must cite the
sources and explain how you get the results. For example, state the Excel function
along with the required parameters when using Excel; describe the detailed steps
when using a hand-held calculator; or provide the URL and detailed steps when
using an online calculator, and so on.
Record your answers and work on the separate answer sheet provided.
This exam has 20 problems; 5% for each problems.
You must include the Honor Pledge on the title page of your submitted final exam.
Exams submitted without the Honor Pledge will not be accepted.
STAT 200: Introduction to Statistics
Final Examination, Spring 2019 OL3
Page 2 of 8
1. You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To
estimate the mean, you collect data from 28 heart patients. Justify for full credit.
(a) Which of the followings is the sample?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two
days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago
(b) Which of the followings is the variable?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two
days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago
2. In order to collect data on the number of courses that your classmates take in this semester, you plan
on asking them: “How many UMUC courses are you taking in this semester? “Justify for full credit.
(a) Which type of d.
mean, variance, and standard deviation of a
discrete probability distribution,binomial probability distribution,hypergeometric probability distribution,Poisson probability distribution.
MATH 106 Finite Mathematics 2152-US1-4010-V1 MATH 106 Finite .docxandreecapon
MATH 106 Finite Mathematics 2152-US1-4010-V1
MATH 106 Finite Mathematics 2152-US1-4010-V1
MULTIPLE CHOICE
1. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 5x + 4y ?
1. _______
A. (0, 4) C. (1, 2)
B. (3, 0) D. (2, 0)
2. Find the equation of the line passing through (1, – 7) and (4, 1): 2. _______
A. 8x + 3y = – 13 B. 2x + y = – 5 C. 2x – y = 9 D. 8x – 3y = 29
3. A survey of 15 randomly selected students responded to the question “How many hours a day do you work on MATH 106?” as follows: 3, 2, 2, 4, 6, 5, 2, 5, 1, 4, 2, 3, 2, 3, 4 . Which histogram below accurately reflects the frequency distribution of the 15 students’ responses?
3. ______
HISTOGRAM A HISTOGRAM C
6
4
2
0
1 2 3 4 5 6
6
4
2
0
1 2 3 4 5 6
HISTOGRAM B HISTOGRAM D
8 6 4
2
0
1 2 3 4 5 6
8 6 4
2
0
1 2 3 4 5 6
4. Identify the single row operation that transforms the matrix as shown: 4. ________
A. 0.5𝑅1 → 𝑅1 C. 𝑅2 + 𝑅1 → 𝑅1
B. 𝑅2 ↔ 𝑅1 D. 3𝑅2 + 𝑅1 → 𝑅1
5. The amount of money you should deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1000 for the next 4 years can be determined using formula for:
5. _______
A. Single-payment, simple interest
B. Single-payment, compound interest
C. Sequence of payments: present value of an ordinary annuity
D. Sequence of payments: future value of an ordinary annuity
6. – 7. The Black Entertainment Television Company (BET) employs copy coordinators and programming analysts. According to company data, a copy coordinator reviews 5 scripts and 3 show schedules per day, whereas a programming analyst reviews 2 scripts and 7 show schedules per day. The company needs enough staff on hand to review at least 12 scripts per day and at least 17 show schedules per day. A copy coordinator makes $230 per day and a programming analyst makes $190 per day. The company wants to minimize daily labor costs. Let x represent number of copy coordinators and y represent number of programming analysts.
6. Identify the daily production constraint for scripts:
6. _______
A. 5𝑥 + 2𝑦 ≤ 12 C. 5𝑥 + 2𝑦 ≥ 12
B. 5𝑥 + 2𝑦 ≤ 17 D. 5𝑥 + 2𝑦 ≥ 17
7. State the objective function.
7. _______
A. 𝐶 = 190𝑥 + 230𝑦
C. 𝐶 = 12𝑥 + 17𝑦
B. 𝐶 = 230𝑥 + 190𝑦
D. 𝐶 = 17𝑥 + 12𝑦
8. In the dice game “Yahtzee”, five-of-a-kind gives the maximum score for a single turn. What is the p
STAT 200 Final ExaminationFall 2019 OL1Page 1 of 11Answer .docxsusanschei
STAT 200 Final Examination
Fall 2019 OL1
Page 1 of 11
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from calculators, programs or software packages without explanation will not be accepted. If you need to use technology to aid in your calculation, you have to cite the source and explain how you get the results. For example, state the Excel function along with the required parameters when using Excel; describe the detailed steps when using a hand-held calculator; or provide the URL and detailed steps when using an online calculator, and so on.
Show all supporting work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
Record your answers and work.
Problem Number
Solution
1
Answer:
(a)
(b)
Justification for (a) and (b):
2
Answer:
(a)
(b)
Justification for (a) and (b):
3
Answer:
(a)
(b)
Justification for (a) and (b):
4
Answer:
(a)
(b)
5
Answer:
(a)
(b)
6
Answer:
(a)
(b)
7
Answer:
(a)
(b)
(c)
Work for (a) and (b):
8
Answer:
(a)
(b)
9
Answer:
(a)
(b)
10
Answer:
(a)
(b)
11
Answer:
(a)
(b)
12
Answer:
(a) n = , p = , and q = .
(b)
(c)
13
Answer:
(a)
(b)
14
Answer:
(a)
(b)
15
Answer:
(a)
(b)
16
Answer:
(a)
(b)
17
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
18
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
19
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
20
Answers:
(a)
(b)
(c)
(d)
STAT 200: Introduction to Statistics
Final Examination, Fall 2019 OL1
1
STAT 200
OL1 Sections
Final Exam
Fall 2019
The final exam will be posted at 12:01 am on October 11, 2019, and
it is due at 11:59 pm on October 13, 2019 Eastern Time.
This is an open-book exam. You may refer to your text and other course materials
for the current course as you work on the exam, and you may use a calculator,
applets, or Excel. You must complete the exam individually. Neither collaboration
nor consultation with others is allowed. It is a violation of the UMUC Academic
Dishonesty and Plagiarism policy to use unauthorized materials or work from
others.
Answer all 20 questions. Mak.
Answer SheetInstructions This is an open-book exam. Yo.docxfestockton
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from calculators, programs or software packages without explanation will not be accepted. If you need to use technology to aid in your calculation, you have to cite the source and explain how you get the results. For example, state the Excel function along with the required parameters when using Excel; describe the detailed steps when using a hand-held calculator; or provide the URL and detailed steps when using an online calculator, and so on.
Show all supporting work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
Record your answers and work.
Problem Number
Solution
1
Answer:
(a)
(b)
Justification for (a) and (b):
2
Answer:
(a)
(b)
Justification for (a) and (b):
3
Answer:
(a)
(b)
Justification for (a) and (b):
4
Answer:
(a)
(b)
5
Answer:
(a)
(b)
6
Answer:
(a)
(b)
7
Answer:
(a)
(b)
(c)
Work for (a) and (b):
8
Answer:
(a)
(b)
9
Answer:
(a)
(b)
10
Answer:
(a)
(b)
11
Answer:
(a)
(b)
12
Answer:
(a) n = , p = , and q = .
(b)
(c)
13
Answer:
(a)
(b)
14
Answer:
(a)
(b)
15
Answer:
(a)
(b)
16
Answer:
(a)
(b)
17
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
18
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
19
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
20
Answers:
(a)
(b)
(c)
(d)
STAT 200: Introduction to Statistics
Final Examination, Fall 2019 OL1
1
STAT 200
OL1 Sections
Final Exam
Fall 2019
The final exam will be posted at 12:01 am on October 11, 2019, and
it is due at 11:59 pm on October 13, 2019 Eastern Time.
This is an open-book exam. You may refer to your text and other course materials
for the current course as you work on the exam, and you may use a calculator,
applets, or Excel. You must complete the exam individually. Neither collaboration
nor consultation with others is allowed. It is a violation of the UMUC Academic
Dishonesty and Plagiarism policy to use unauthorized ma ...
Answer all 20 questions. Make sure your answers are as complet.docxfestockton
Answer all 20 questions. Make sure your answers are as complete as possible, particularly when it asks for you to show
your work. Answers that come straight from calculators, programs or software packages without any explanation will
not be accepted. If you need to use technology (for example, Excel, online or hand-held calculators, statistical packages)
to aid in your calculation, you must cite the sources and explain how you get the results. For example, state the Excel
function along with the required parameters when using Excel; describe the detailed steps when using a hand-held
calculator; or provide the URL and detailed steps when using an online calculator, and so on.
Record your answers and work on the separate answer sheet provided.
This exam has 20 problems; 5% for each problems.
STAT 200: Introduction to Statistics
Final Examination, Fall 2019 OL1
1. You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To estimate the
mean, you collect data from 28 heart patients. Justify for full credit.
(a) Which of the followings is the sample?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago
(b) Which of the followings is the variable?
(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
(ii) Cholesterol level of the person recovering from heart attack suffered two days ago
(iii) Set of all patients recovering from a heart attack suffered two days ago
(iv) Set of 28 patients recovering from a heart attack suffered two days ago
2. Choose the best answer. Justify for full credit.
(a) The Knot.com surveyed nearly 13,000 couples, who married in 2017, and asked how much they spent on their
wedding. The average amount of money spent on was $33,391. The value $33,391 is a:
(i) parameter
(ii) statistic
(iii) cannot be determined from information provided.
(b) A marketing agent asked people to rank the quality of a new soap on a scale from 1 (poor) to 5 (excellent). The level
of this measurement is
(i) nominal
(ii) ordinal
(iii) interval
(iv) ratio
3. True or False. Justify for full credit.
(a) If the variance from a data set is zero, then all the observations in this data set must be identical.
(b) The median of a normal distribution curve is always zero.
4. A STAT 200 student is interested in the number of credit cards owned by college students. She surveyed all of her
classmates to collect sample data.
(a) What type of sampling method is being used?
(b) Please explain your answer.
5. A study was conducted to determine whether the mean braking distance of four-cylinder cars is greater than th ...
This is an open-book exam. You may refer to your text and other .docxchristalgrieg
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others.
Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your supporting work and reasoning. Answers that come straight from calculators, programs or software packages without any explanation will not be accepted. If you need to use technology (for example, Excel, online or hand- held calculators, statistical packages) to aid in your calculation, you must cite the sources and explain how you get the results.
Record your answers and work on the separate answer sheet provided.
This exam has 100 total points; 5 points for each question.
You must include the Honor Pledge on the title page of your submitted final exam. Exams submitted without the Honor Pledge will not be accepted.
Page 1 of 8
1. True or False. Justify for full credit.
(a) A is an event, and Ac is the complement of A, then P(A OR Ac ) = 0.
(b) If the variance of a data set is 0, then all the observations in this data set must be identical.
(c) If a 95% confidence interval for a population mean contains 1, then the 99% confidence interval for the same parameter must contain 1
(d) When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8.
(e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.
2. Choose the best answer. Justify for full credit.
(a) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2015. 100 students graduated from UMUC in 2015 were randomly selected, and the average GPA for the group is 3.5. The value 3.5 is a
(i) statistic
(ii) parameter
(iii) cannot be determined
(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(c) In a career readiness research, 100 students were randomly selected from the psychology program, 150 students were randomly selected from the communications program, and 120 students were randomly selected from cyber security program. This type of sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
3. Choose the best answer. Justify for full credit.
(a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. ...
probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty. probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.,probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for grade 10 m athematics. statistics and probabilty.probailkity of compound evengts . for gr
1. True or False. Justify for full credit. .docxKiyokoSlagleis
1.
True or False.
Justify for full credit.
(15 pts)
(a) If the variance of a data set is zero, then all the observations in this data set are zero.
(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.
(c) Assume X follows a continuous distribution which is symmetric about 0. If , then .
(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.
(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic
follows a Student’s t
-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .
Refer to the following frequency distribution for Questions 2, 3, 4, and 5.
Show all work. Just the answer, without supporting work, will receive no credit.
The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.
Checkout Time (in minutes)
Frequency
Relative Frequency
1.0 - 1.9
3
2.0 - 2.9
12
3.0 - 3.9
0.20
4.0 - 4.9
3
5.0 -5.9
Total
25
2.
Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places. (5 pts)
3.
What percentage of the checkout times was at least 3 minutes? (3 pts)
4.
In what class interval must the median lie? Explain your answer. (5 pts)
5.
Does this distribution have positive skew or negative skew? Why? (2 pts)
Refer to the following information for Questions 6 and 7.
Show all work. Just the answer, without supporting work, will receive no credit.
Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)
6.
If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (5 pts)
STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL1/US1 Page 3 of 6
7.
If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (5 pts)
Refer to the following situation for Questions 8, 9, and 10.
The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students.
Minimum
Q1
Median
Q3
Maximum
Quiz 1
15
45
55
85
100
Quiz 2
20
35
50
90
100
For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then
explain
your answer in
each
case.
(4 pts each)
8.
Which quiz has less interquartile range in grade distribution?
9.
Which quiz has the greater percentage of students with grades 90 and over?
10.
Which quiz has a greater percentage of students with grades less than 60?
Refer to the following informati.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
1. Business Statistics (BUS 505) Assignment 5
7) A company knows that a rival is about to bring out a competing product. It believes that this
rival has three possible packaging plans (superior, normal, cheap) in mind and that all are
equally likely. Also there are three equally likely possible marketing strategies (intense media
advertising, price discount, and use coupon to reduce the price of future purchases). What is the
probability that the rival will employ superior packaging in conjunction with an intense media
advertising campaign? Assume that packaging plans and marketing strategies are determined
independently.
Answer: Let, A denote that one of the packaging plan in use
B denote that one of the marketing strategies in use
So, Probability distribution for packaging plan;
Ai A1 A2 A3
P(Ai)
1
3
1
3
1
3
And, Probability distribution for marketing strategies;
Bi B1 B2 B3
P(Bi)
1
3
1
3
1
3
P(A1 ÇB1)= P(A1)P(B1)
P((A1 ÇB1)= 1 X 3
3
1 = 9
1 =.111
8) A financial analyst was asked to evaluate earnings prospect for seven corporations over the
next year, and to rank them in order of predicted earnings growth rates.
a. How many different rankings are possible?
b. If, in fact, a specific ordering is simply guessed, what is the probability that is guess will turn
out to be correct?
Answer:
Given that, evaluate earnings prospect for seven corporations over the next year.
a) The possible number of different rankings is: 7! = 7´6´5´4´3´2´1 =5040
b) A specific ordering is simply guessed. So, the probability that this guess will turn out to be
correct is: 1/7! = 1/5040
9) A company has fifty sales representatives. It decides that the most successful representatives
during the previous year will be awarded a January vacation in Hawaii, while the second most
successful will win a vacation in Las Vegas. The other representatives will be required to attend a
conference on modern sales methods in Buffalo. How many outcomes are possible?
Answer:
Given that, a company has fifty sales representatives.
So, the possible numbers of outcomes are: 50p2 X 48c48 = 2450X1 =2450
1
2. Business Statistics (BUS 505) Assignment 5
10) A securities analyst claims that given a specific list of six common stocks, it is possible to
predict, in the correct order the three that will perform best during the coming year. What is the
possibility of making the correct selection by the chance?
Answer:
Given, n = 6 and, x = 3
The possible numbers of making the correct selection of 3 common stock out of the 6
6!
common stock are: 6p3 = (6 - 3)!
= 120
1
The probability of making the correct selection by chance is: P (6p3) = 120
11) A student committee has six members-four undergraduates and two graduate students. A
subcommittee of three members is to be chosen randomly, so that each possible combination of
three of the six students is equally likely to be selected. What is the probability that there will be
no graduate students on the subcommittee?
Answer:
Given that, n = 6 (four undergraduate and two graduate students)
x = 3
The total numbers of possible combination of three numbers chosen or selected from six numbers
are:
6!
- = 20
6c3 = 3!(6 3)!
Now, no graduate students are on the subcommittee. So, the 3 numbers must come from 4
4!
undergraduate members. The number of such combination is: 4c3 = 3!(4 - 3)!
= 4
The probability that there will be no graduate students on the subcommittee is:
c = 20
4 3
c
6 3
4 = 5
1 or 0.2
12) Baseball’s American league East has five teams. You are required to predict, in order the top
three teams at the end of the session. Ignoring the possibility of ties calculate the number of
different predictions you could make .what is the probability of making the current prediction by
chance?
Answer: Given that, n = 5 and x = 3
The total numbers of possible predict the top three teams chosen from the five teams are:
5!
5p3 = (5 - 3)!
= 60
1 =.017
Now, the probability of making the correct prediction by chance: P (5p3) = 60
13) A manager has four assistants-johns, George, Mary and jean-to assign to four tasks. Each
assistant will be assi8gn to one of the tasks, one assistant to each task:
2
3. Business Statistics (BUS 505) Assignment 5
a. How many different arrangements of assignments are possible?
b. if assignments are made at random , what is probability that Mary will be assigned to a
specific task?
Answer: Given that, n = 4 and x = 4
4!
- =24
a) the total number of possible arrangement of assignment is: 4p4 = (4 4)!
c p
1 1*3 3
b) the probability that mary will be assigned to a specific task: 4 p
4
6 = 4
= 24
1 =.25
14) The senior management of corporation has decided that in the future, it wishes to divide its
advertising budget between two agencies. Eight agencies are currently being considered for this
work .How many different choices of two agencies are possible?
Answer: Given that, n = 8 and x = 2
8!
- = 28
Two agencies could be select 8c2 = 2!(8 2)!
15) You are one of seven female candidates auditioning for two parts- the heroine and her best
friend – in a play. Before the auditions, you know nothing of the other candidates, and assume all
candidates have equal chances for either part.
(a) How many distinct choice are possible for casting the two parts?
(b) In how many of the possibilities in (a) would you be chosen to play the heroine?
(c) In how many of the possibilities in (a) would you be chosen to play her best friend?
(d) Use the results in (a) and (b) to find the probability you will be chosen to play the
heroine. Indicate a more direct way of finding this probability?
(e) Use the results in (a), (b), and (c) to find the probability you will be chosen to play the
one of the two parts. Indicate a more direct way of finding this probability?
Answer:
Given that, n=7 and x= 2
7!
- =42
(a) The possible distinct choices for casting two parts; 7p2 = (7 2)!
(b) The possibilities to play the heroine are; (1c1)´(6c1)= 6
(c) The possibilities to play her best friend; (1c1)´(6c1)= 6
1 p 1 ´ 6 p
1
(d) P(H) = 7 p
2
6 = 7
= 42
1
(e) P(AÈ B) = P(A)+P(B)-P(A Ç B)
1 + 7
= 7
1 - 7
0
3
4. Business Statistics (BUS 505) Assignment 5
2
= 7
16) A work crew for a building project is to be made up of two craftsmen and four laborers
selected from a total of five craftsmen and six laborers available.
a. How many different combinations are possible?
b. the brother of one of the craftsmen is a laborer. if the crew is selected at random, what is
the probability that both brothers will be selected.
c. what is the probability that neither brother will be selected?
Answer:
a. The possible combination for work crew is; (5c2) ´ (6c4) =150
b. The probability that both brother will be selected are; (1c1) (4c1) ´(1c1) (5c3) =40
(1 c 1)(4 c 1) ´ (1 c 1)(5 c
3)
The probability is = 40 (5 c 2)(6 c
4)
=.27
= 150
c. The probability that neither brother will be selected are; (1c0)(4c2) ´(1c0) (5c4) =6´5=30
(1 c 0)(4 c 2) ´ (1 c 0)(5 c
4)
The Probability is= 30 (5 c 2)(6 c
4)
=.2
=150
17) A mutual fund company has six funds that invest in the U. S. market, four that invest in
foreign markets. A customer wants to invest in two U.S. funds & two foreign funds.
a. How many different sets of funds from this company could the investor choose?
b. Unknown to this investor, one of the U.S. funds & one of the foreign funds will seriously
under-perform next year. If the investors select funds for purchase at random, what is the
probability that at least one of the chosen funds will seriously under-perform next year?
Answer:
Given that; Company has 6 funds invest in U.S market
Company has 4 funds invest in foreign market
(a) The possible set of funds from this company are; 6C2 * 4C2 = 90
(1 c 0)(5 c 2) ´ (1 c 0)(3 c
2)
(b) P(N)= (6 c 2)(4 c
2)
30 = 3
= 90
1
1 = 3
P(A)=1- P(N)= 1- 3
2
18) It was estimated that 30% of all seniors on a campus were seriously concerned about
employment prospects, 25% were seriously concerned about grades, and 20% were seriously
concerned about both .what is the probability that a randomly chosen senior from this campus is
seriously concerned about at least one of this two things?
Answer:
A=30% or .3; B=25% or .25; A Ç B=20% or .2
4
5. Business Statistics (BUS 505) Assignment 5
P (AÈ B) =P (A) +P (B) P - P (AÇ B)
=30%+25%-20%
=35%
19) A music store owner finds that 30% of customers entering the store ask an assistant for help
and that 20% make a purchase before leaving. It also found that 15% of all customers both ask
for assistant and make a purchase. What is the probability that a customer does at least one of
these two things?
Answer: Let,
A denotes “Customer entering the store ask an assistant for help”
B denotes “Customer entering the store make a purchase before leaving”
Given that,
P (A) =30% or .30, P (B) =25% or .25, P (A B) =15% or .15 and P (A B) =?
We know that,
P (A B) = P (A) + P (B) - P (A B)
= .30 +. 20 - .15
= .35
20) Refer to the information in Exercise 19, and consider the two events “customer ask for
assistance” and “customer makes purchase.” In answering the following questions, provide
reasons expressed in terms of probabilities of relevant events.
(a) Are the two events mutually exclusive?
(b) Are the two events collectively exhaustive?
(c) Are the two events statistically independent?
Answer:
a) The two events A and B are not mutually exclusive. Because, P (A B) not equal to 0.
b) The two events A and B are not collectively exhaustive. Because,
P(A B) not equal to P (S) = 1.
c) The two events A and B are not statistically independent. Because, P (A) P (B) not equal to P
(A B).
22) A mail - order firm considers three possible foul – ups in filling an order:
A: The wrong item is sent.
B: The item is list in transit.
C: The item is damaged in transit.
Assume that event A is independent of both B and C and that events B and C are mutually
exclusive. The individual event probabilities are P(A) = .02, P(B) = .01, and P(C) = .04. Find the
probability that at least one of these foul – ups occurs for a randomly chosen order.
Answer: Let,
A = “The wrong item is sent”
B = “The item is lost in transit”
5
6. Business Statistics (BUS 505) Assignment 5
C = “The item is damaged in transit”
Given that, P (A) = .02 P (B) = .01 P(C) = .04
Since, Event A is independent of both B and C
P (A B) = P (A) ´ P (B)
= .02 ´ .01
= .0002
And P (A C) = P (A) ´ P(C)
= .02 ´ .04
= .0008
Given that, B and C are mutually exclusive. P (B C) = 0
P (A B C) = P (A) + P (B) + P(C) - P (A B) – P (B C) – P(C A) + P (A B C)
= .02 + .01 + .04 - 0.0002 – 0 - 0.0008 + 0 = 0.069
23) A coach recruits for a college team a star player who is currently a high school senior. In
order to play next year, the senior must both complete high school with adequate grades and pass
a standardized test. The coach estimates that the probability the athlete will fail to obtain
adequate high school grader is .02, the probability the athlete will not pass the standardized test
is .15, and that these are independent events. According to these estimates, what is the probability
this recruit will be eligible to play in college next year?
Answer:
Let,
A = “The athlete received adequate grade”
B = “The athlete passes the standardize test”
So, Given that, P ( A ) = 0.02 and, P ( B ) = 0.15
P (A) = 1 – P ( A ) P (B) = 1 - P ( B )
= 1- 0.02 = 1 – 0.15
= 0.98 = 0.85
Since, A and B are independent events. So, A and B are also independent.
P (A B) = P (A) ´ P (B)
= 0.98 ´ 0.85
= 0.833
So, the probability for this recruit will be play in the next year is 0.833.
24) Market research in a particular city indicated that during a week 18% of all adults watch a
television program oriented to business and financial issues, 12% read a publication oriented to
these issues, and 10% do both.
a) What is the probability that an adult in this city, who watches a television program
oriented to business and financial issues, reads a publication oriented to these issues?
b) What is the probability that an adult in this city, who reads a publication oriented to
business and financial issues, watches a television program oriented to these issues?
Answer: Let,
A = “Adults watch a TV program oriented to business & financial issues”
B = “Adults read a publication oriented to business and financial issues”
6
7. Business Statistics (BUS 505) Assignment 5
Given that, P (A) = .18 P (B) = .12 P (A B) = .10
P A B
( ) = .10
=
P A
a) P (B/A) = 0.56
.18
( )
P A B
( ) = .10
=
P B
b) P (A/B) = 0.83
.12
( )
25) An inspector examines item coming from an assembly line .A review of her record reveals
that she accepts only 8% of all defect items. It was also found that 1% of all items from the
assembly line are both defective and accepted by the inspector. What is the probability that a
randomly chosen item from this assembly line is defective?
Answer:
Let
A denotes “An assembly line product is defective”.
B denotes “An assembly line product is accepted”.
So,
P(B / A) =.08 P(AÇB) =.01
We Know that,
P B A P A B
( / ) ( )
P A
P A = P A Ç
B
( ) ( )
( / )
( ) .01
.08
=
P A
( ) 0.125
( )
=
= Ç
P A
P B A
So, the probability of randomly chosen item from this assemble line product is defect is 0.125
26) An analyst is presented with least of four stocks and five bonds .He is asked to predict, in
order the two stocks that will yield that highest return over the next year and the two bonds that
will have the highest return over the next year. Suppose that these predictions are made randomly
and independently of each other. What is the probability that the analyst will be successful in at
least one of the two tasks?
Answer: Let,
S is denote Stock and B is denote Bond
S=4p2=12 P (S) = 12
1 B=5p2=20 P (B) = 1
20
7
8. Business Statistics (BUS 505) Assignment 5
1 ´ 20
P (SÇ B) = 12
1 = 1
240
P (SÈ B) =P (A) +P (B) -P (AÇ B)
1 + 20
=12
1 - 1
240
20 +12 +1
=.129
= 240
27) A bank classifies borrowers as high risk or low risk. Only 15% of its loans are made to those
in the high risk category .of all its loans, 5% are in default, and 40% of those in default are to
high risk borrowers. What is the probability that a high risk borrower will default?
Answer:
Let,
H denote ‘High risk category borrowers’
D denote ‘In default are to high-risk borrowers’
So, P(H)=.15 P(D)=.05 P(H I D)=.40
Now,
P ( HID ) P ( D
)
P(D I H)= .40´.05 P ( H
)
=.133
= .15
28) A conference began at noon with two parallel sessions. The session on portfolio management
was attended by 40% of the delegates, while the session on Chartism was attended by 50%. The
evening session consisted of a talk titled “is the random walk dead?” This was attended by 80%
of delegates.
a) If attendance at the session on portfolio management and Chartism was mutually exclusive,
what is the probability that a random chosen delegate attended at least one of the session?
b) If attendance of the portfolio management and evening sessions are statistically
independent, what is the probability that a randomly chosen delegate attended at least one of the
session?
c) Of those attending the Chartism session, 75% also attended the evening session. What is the
probability that a randomly chosen delegate attended at least one of these two sessions?
Answer:
Let
A denote be the probability on portfolio management
B denote be the probability on Chartism
C denote be the probability on all delegates
Given that, P(A)=.40 P(B)=.50 P(C)=.80
(a) P(A B)= P(A)+P(B)-P(A B)
= .40+ .50 -0
= .90
8
9. Business Statistics (BUS 505) Assignment 5
(B) the portfolio management and evening sessions are statistically independent
So, P(A C)= P(A)+P(C)-P(A C)
=.40+.80-P(A)P(C)
=1.20-(.40*.80)
=1.20-.32
=.88
(C) Here, Of those attending the Chartism session, 75% also attended the evening session.
So, P(C I B)= .75
P(B C)= P(B)+P(C)-P(B C)
=.50+.80- P(B)P(C)
=1.30- (.50 X .75)
=1.30- .375
=.925
=92.5%
29) A stock market analyst claims expertise in picking stocks that will outperform the
corresponding industry norms. This analyst is presented with a list of five high technology stocks
and a list of five airlines stock, and she is invited to nominate, in order the three stocks that will
do best on each of these two lists over the next year. The analyst claims that success in just one of
these two tasks would be a substantial accomplishment .If, in fact, the choices were made
randomly and independently, what would be the probability of success in at least one of the two
tasks merely by chance? Given this result, what do you think of the analysts claim?
Answer:
1
A=5p3=60 P (A) = 60
1
B=5p3=60 P (B) = 60
1 ´ 60
(AÇ B)=P (A) +P (B) = 60
1 = 1
3600
P (AÈ B) =P (A) +P (B) P - P (AÇ B)
1 + 60
= 60
1 - 1
3600
119 or .033055555
= 3600
I think that the analyst claim is not right.
30) A quality control manager found that 30% of worker- related problems occurred on
Mondays, and that 20% occurred on the last hour of a day’s shift. It was also found that 4% of
worker -related problem occurred in the last hour of Monday’s shift.
a) What is the probability that a worker- related problem that occurs on a Monday does not
occur in the last hour of the days shift?
b) Are the events “Problems occur on Monday” and “problem occurs on last hour of the day’s
shift” statistically independent?
9
10. Business Statistics (BUS 505) Assignment 5
Answer:
Let,
A denote “worker related problem occur on Monday”
B denote “worker related problem in last hour of a day shift”
So, P(A)= .30 P(B)=.20 P(A B)=.04
P A B Here, P(B) = 1-P(B) =1- .20 =.80
( )
P A
(a) P (B A) = ( )
.26 We know, P (A) = P(A B)U
= .30
P(A B)
=.867 So, .30 = .04+ P(A B)
Þ P(A B) = .30-.04
Þ P(A B) =.26
(b) P(A B)=P(A) P(B)
P(A B)= .30X.20
P(A B)= .06
Þ.04 ¹ .06
So, P(A B) ¹ P(A)P(B)
So, the two events are not statistically independent. Because P(AÇB) ¹P(A)´P(B) .
31) A corporation was concerned about the basic educational skills of its workers and decided to
offer a selected group of them separate classes in reading and practical mathematics. Forty
percent of these workers signed up for the reading classes, and 50% for the practical
mathematics classes. Of those signing up for reading classes, 30% signed up for the mathematics
classes.
(a)What is the probability that a randomly selected worker signed up for both classes?
(b)What is the probability that a randomly selected worker who signed up for the
mathematics classes also signed up for the reading classes?
(c)What is the probability that a randomly chosen worker signed up for at least one of
these two classes?
(d)Are the events “Signs up for reading classes” and “Signs up for mathematics classes”
statistically independent?
Answer: Let, A denotes that “Classes in reading.”
B denotes that “Classes in practical mathematics.”
Given that, P(A)= .40 P(B)= .50 P(B I A)=.30
P A B = ]
( )
P B
(a) P(A B)= P(A) P(B I A) [P(A I B)= ( )
= .40 ´ .30
10
11. Business Statistics (BUS 505) Assignment 5
=.12
P A B =
( )
P B
(b) P(A I B) ( )
P BIA P A
( ) ( )
P B
= ( )
.30´.40 =.24
= .50
(c) P(AUB)= P(A)+P(B)-P(A B)
=.40+.50-P(A)P(B I A)
=.90- (.40´.30)
=.90-.12 =.78
(d) P(A B)=P(A)P(B)
P(A B)=.40´.50
P(A B)=.20
But, .12 ¹ .20
So, this two events are not statistically independent because they are not P(A B)= P(A)P(B).
32) A lawn care service makes telephone solicitation, seeking customers for the coming season. A
review of the records indicated that 15%of these solicitations produced new customers, and that,
of these new customers. 80% had used some rival service in the previous year. It was also
estimated that, of all solicitation call made. 60% were to people who had used a rival service the
previous year.
What is the probability that a call to a person who used a rival service the previous year will
produce a new customer for the lawn care service?
Answer:
Given that, P(A)= .15 P(B I A)= .80 P(B)= .60
P ( A B )
P(A I B) =
P ( B
)
P A P B A
( ) ( )
P B
= ( )
.15´.80 = .60
= .60
.12 =.20
33) An editor may use all, some, or none of three possible strategies to enhance the sales of a
book:
A: An expensive prepublication promotion
B: An expensive cover design
C: A bonus for sales representatives who meet predetermined sales levels
In the past, these three strategies have been applied simultaneously to only 2% of the company’s
books. Twenty percent of the books have had expensive cover designs, and of these, 80% have
had expensive prepublication promotion. A rival editor learns that a new books is to have both
11
12. Business Statistics (BUS 505) Assignment 5
expensive prepublication promotion and cover design and now wants to know how likely it is that
a bonus scheme for sales representatives will be introduced. Compute the probability of interest
to the rival editor.
Answer:
Given,
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