FOR MORE CLASSES VISIT www.tutorialoutlet.com Show your work. You may use your book, notes, and other resources I have provided. You must not work with another person on this exam. If I have evidence that you worked or copied someone else’s work you may lose all points for that problem or potentially you will receive a zero on the exam; that goes for the other person as well. To avoid this potential problem, do not take this exam with someone else; do not talk about the problems in this exam with someone else. Instead, you can use problems from the homework as a conduit if needed. Do not compare answers with someone else. Write out values to four decimal places if the decimal representation does not terminate after four decimals. For situations you can write the values using fractions you can leave the answer in unreduced fraction form.

1. Show your work. You may use your book, notes, and other
resources I have provided. You must not work with
another person on this exam
FOR MORE CLASSES VISIT
www.tutorialoutlet.com
Show your work. You may use your book, notes, and other resources I have
provided. You must not work with another person on this exam. If I have
evidence that you worked or copied someone else’s work you may lose all
points for that problem or potentially you will receive a zero on the exam; that
goes for the other person as well. To avoid this potential problem, do not take
this exam with someone else; do not talk about the problems in this exam with
someone else. Instead, you can use problems from the homework as a conduit if
needed. Do not compare answers with someone else. Write out values to four
decimal places if the decimal representation does not terminate after four
decimals. For situations you can write the values using fractions you can leave
the answer in unreduced fraction form.
1. To diagnose colorectal cancer, the hemoccult test- among others- is
conducted to detect occult blood in the stool. This test is used from a particular
age on, but also in routine screening for early detection of colorectal cancer.
Imagine you conduct a screening using the hemoccult test in a certain region.
For symptom-free people over 50 years old who participate in screening using
the hemoccult test, the following information is available for this region:
The probability that one of these people has colorectal cancer is 0.3% (please be
careful converting this to a decimal). If a person has colorectal cancer, the
probability is 93.5% that the person will have a positive hemoccult test. If a
person does not have colorectal cancer, the probability is 2.1% that the person
will have a positive hemoccult test.

2. a) [3] Imagine a person (over age 50, no symptoms) who has a positive
hemoccult test in your screening. What is the probability that this person
actually has colorectal cancer? Write the question using function notation.
b) [3] If a person over age 50 years has a hemoccult test performed what is the
probability that it is negative? Write the question using function notation.
2. [3] KGW News Channel 8 interviews nine Portland residents at random and
asks them if they will vote for the incumbent Oregon governor this coming
November. Let the random variable X measure the number of people who will
vote for the incumbent governor. Write out the sample space of the random
variable X.
3. [3] The random variable X is uniformly distributed, such that 15 ≤ X ≤ 42.
Calculate the following
P(X > 22 AND X < 35) =
4. [3] You are told that P(A) = 0.4 , P (B) = 0.3 and that the two events are
independent. Calculate P(A OR B).
5. [3] You are told that events A, B are disjoint, with P(A) = 0.4 P(B) = 0.3.
What is P(A and B) ?
6. Scores on the mathematics part of the SAT college entrance for a particular

3. year derive a population mean value of 523, µ, with a population standard
deviation, σ, of 112. While on the verbal part of the SAT for that same year is µ
= 504, σ = 105. Let the variable X define a math score on the SAT, and let Y
define a verbal score on the SAT. Furthermore define the variable T to be the
total SAT score, the sum of each part of the exam; T = X + Y.
a. [3] Calculate E(X +Y)
b. [3] Calculate SD(X + Y) to two decimal places.
7. [3] In a drawer I have five batteries three that work and two that do not work.
If I grab three batteries, what is the probability that only one works.
8. A game of chance consists of drawing one card out of ten at random. One
card contains the number 100, in which a person, if they chose that card wins
$100. A second card contains the number 20, if they chose that card the person
wins $20. If any other card is chosen the person losses $16. The game is then
played by shuffling cards, facing them down, and having the person choose a
card while face down. Once the card is chosen, the outcome is determined, and
the card is put back and the deck reshuffled so one can play again.
Let the random variable X equal the amount of money won or lost.
X
$100
$20
-$16

4. P(X = x)
0.1
0.1
0.8
a. [3] What is the probability that a person loses two games in a row?
b. [3] On average what does the person expect to win or lose in the long run per
game?
c. [3] Calculate s, which is SD(X) to the nearest cent.
9. [3] A car dealership sells 58% of its cars to women. At that same car
dealership 40% of car sales are minivans. Therefore a salesman calculates that
23.2% of the minivans are sold to women. What assumption did the salesman
make to come up with this value?
10. [3] You are provided with the following information P(A) = 0.3 , P(B) = 0.2,
P(A OR B) = 0.44 and that the events are independent. What is P(A | B)?
Age

5. Under 30
30 - 49
Over 50
Total
Blood Pressure
Low
122
432
300
854
Normal

6. 501
122
205
828
High
250
102
151
503

7. Total
873
656
656
2185
11. A school offered blood pressure screening for its employees. The results are
shown in the table.
a. [4] We choose an employee at random, what is the probability that this person
is a 30 to 49 year old with normal blood pressure? Write the question also in
function notation along with the appropriate mathematical symbols, equal signs,
to communicate your work.
b. [4] If an employee is over the age of 50, what is the probability that their
blood pressure is high?
Write the question also in function notation along with the appropriate
mathematical symbols, equal signs, to communicate your work.
Age
Under 30

8. 30 - 49
Over 50
Total
Blood Pressure
Low
122
432
300
854
Normal

9. 501
122
205
828
High
250
102
151
503
Total

10. 873
656
656
2185
11. A school offered blood pressure screening for its employees. The results are
shown in the table.
c. [3] Are the events a person is Over 50, a person has high blood pressure
independent events?
You must show work that leads to the conclusion that yes the events are
independent, or no, the events are not independent along with the statement
whether the events are independent or not. Approximate to three decimal places
to make your conclusion.
12. Comparison studies, such as which battery last longest or which aspirin
works the best, makes one assumption as to what reality looks like. The
assumption is that we have equality among the items we are comparing that is
the items are equally good. What follows is the start of the model that is
eventually constructed. Consider the random variable X which measures the
weight of a coconut. The mean weight is 1.44 kg, and standard deviation of 0.23

11. kg. I randomly choose two coconuts, measure their weight individually, then
subtract the weight;
S = X – X.
a. [3] Find the value of E(S) =
b. [3] Find the value of SD(S) =
13. In a particular state university, 42% of students major in STEM fields
(Science, Technology, Engineering and Mathematics). Of the students majoring
in STEM fields 44% graduate in four years or less, while 52% of students in
non-STEM related fields graduate in four years or less.
a. [3] What is the probability that a student chosen at random
graduates in four years or less.
b. [3] If a student takes more than four years to graduate, what is the probability
that they majored in a STEM field?
c. [3] Find P(Graduate ≤ 4 | Non-stem field) =
d. [3] What is the probability that a student chosen at random is in a STEM field
and takes more than four years to graduate?
14. [3] Shade in the area that corresponds to P(A OR B)

12. 15. [3] Shade in the area that corresponds to P(NOT A AND NOT B)
16. [5] You roll a six-sided fair die. If it comes up a 6, you win $100 and that
ends the play. However, if your first throw is not a 6 you get to roll again. If on
the second throw you get a 6, then you win $50 and that ends the play. If you
don’t roll a six on the second roll you lose $25, and the play ends.
Let the random variable Y equal the amount of money won or lost on one play
(a play consist of rolling the die until you win or lose money). Create a
probability table for all the outcomes of the random variable Y.
Y
P(Y = y)
17. [3] If I toss a die four times what is the probability that it lands on six all
four times?
18. [3] In Iceland 56% of the population hast O type blood. If four people are
chosen at random what is the probability that at least one person has O type
blood in the sample of four?
19. Motor vehicles sold to individuals (non-commercial) in the U.S. are
classified as either cars or light trucks (Light does not mean small, but rather
that it is not a commercial truck. For example, an SUV is considered a light
truck) and as either domestic or imported. In early 2004, 69% of vehicles sold
were light trucks, 78% were domestic, and 55% were domestic light trucks.
a. [3] Write the probability of 55% using function notation and the correct
conjunction.
b. [3] A vehicle is chosen at random, what is the probability that it is domestic
but not a light truck?
20. [3] At a community college 28% of students work full time while attending

13. school. Of the students working full time while attending school, 40% receive
financial aid. At this same community college 59% of students receive financial
aid. What is the probability that a student at this community college works full
time and receives financial aid?
21. [4] Let the variable X measure the amount of liquid dispensed by a faulty
soda dispensing machine at a factory.
Suppose that the mean amount of soda dispensed is 2980ml, with a standard
deviation of 25 ml. Furthermore, the distribution of the amount of liquid
dispensed is normal. What is the probability that either the dispensing machine
dispenses less than 2950 ml or more than 3000ml? Show work using function
notation correctly to communicate your steps, along with conversion to a z-
score.
22. Consider the random variable X which measures the weight of a coconut.
The mean weight is 1.44 kg, and standard deviation of 0.23 kg.
a. [3] Consider the random variable T consisting of choosing five coconuts at
random, measuring each coconut weight individually and totaling the weight; T
= X + X + X + X + X. Find E(T).
b. [3] Consider the random variable T consisting of choosing five coconuts at
random, measuring each coconut weight individually and totaling the weight; T
= X + X + X + X + X. Find SD(T).