PROBABILITY Probability of A P(A)= NF/NP Addition rule P(A or B) = P(A) + P(B) – P(A and B) Multiplication rule P(A and B) = P(A) . P(B\A) Complementary principle P(A)+P(A’)=1 Independency P(A)=P(A\B) P(B)=P(B\A) NUMERICAL MEASURES PCS= outliers 2k>n PROBABILITY DISTRIBUTIONS 1. The following is the time, in minutes, 15 employees of accounting department of East Penn Manufacturing spent commuting to work this morning. [20pts] 28 25 48 37 41 19 32 26 16 23 23 29 36 31 26 1. Organize data into stemplot. [2pts] 1. Find the standard deviation, round it to 2 decimal places. [3pts] 1. Find value of the 85th percentile L85 (or P85) and write its brief interpretation. [3pts] 1. Find Q1, Q3, IQR and test possible outliers. Draw a conclusion clearly. [5pts] 1. Organize data into classes using an interval 15-23 as the first. [2pts] 1. What is a class width w in previous part e? [1pt] 1. Use the frequency table and find the standard deviation. Round the result to two decimal places if necessary. [3pts] 1. Compare results of b) and g). Which one is exact? [1pt] _________________________________________________________________________________ 2.Use the frequency table and find the median. Round only the last result to two decimal places. [4pts] Class frequency 0-4 6 5-9 7 10-14 12 15-19 8 _________________________________________________________________________________ 3. Grace Andrews, a stockbroker, recommends two stocks (Hewlett Packard and Citibank) to her customers. Suppose that the probability that each stock’s price will go up next year is 0.6, and that each stock’s price behavior is independent of the price behavior of the other stock. Take a number of stocks that will go up next year as the random variable X and give a complete probability distribution.[6pts] 4. A survey of executives dealt with their loyalty to the company. One of the questions was, “If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?” The responses of the 200 executives in the survey were cross-classified with their length of service with the company. Give all results rounded to 4 decimal places.[2+3+2+3+1+5=16pts] LENGTH OF SERVICE LOYALTY < 1year 1-5 years 6-10years >10years total Would remain 10 30 5 75 120 Would not remain 25 15 10 30 80 total 35 45 15 105 200 a) What is the probability that randomly chosen executive is loyal to the company? b) What is the probability that randomly chosen executive has more than 10 years of service OR is not loyal to the company? c) What is the probability that randomly chosen executive has less than one year of service AND is not loyal to the company? d) Two executives are chosen ra.

1. PROBABILITY
Probability of A P(A)= NF/NP
Addition rule P(A or B) = P(A) + P(B) – P(A and B)
Multiplication rule P(A and B) = P(A) . P(BA)
Complementary principle P(A)+P(A’)=1
Independency P(A)=P(AB) P(B)=P(BA)
NUMERICAL MEASURES
PCS=
outliers
2k>n
PROBABILITY DISTRIBUTIONS

2. 1. The following is the time, in minutes, 15 employees of
accounting department of East Penn Manufacturing spent
commuting to work this morning. [20pts]
28 25 48 37 41 19 32 26 16 23 23 29 36 31 26
1. Organize data into stemplot. [2pts]
1. Find the standard deviation, round it to 2 decimal places.
[3pts]
1. Find value of the 85th percentile L85 (or P85) and write its
brief interpretation. [3pts]

3. 1. Find Q1, Q3, IQR and test possible outliers. Draw a
conclusion clearly. [5pts]
1. Organize data into classes using an interval 15-23 as the first.
[2pts]
1. What is a class width w in previous part e? [1pt]
1. Use the frequency table and find the standard deviation.
Round the result to two decimal places if necessary. [3pts]

4. 1. Compare results of b) and g). Which one is exact? [1pt]
_____________________________________________________
____________________________
2.Use the frequency table and find the median. Round only the
last result to two decimal places. [4pts]
Class
frequency
0-4
6
5-9
7
10-14
12
15-19
8
_____________________________________________________
____________________________

5. 3. Grace Andrews, a stockbroker, recommends two stocks
(Hewlett Packard and Citibank) to her customers. Suppose that
the probability that each stock’s price will go up next year is
0.6, and that each stock’s price behavior is independent of the
price behavior of the other stock. Take a number of stocks that
will go up next year as the random variable X and give a
complete probability distribution.[6pts]
4. A survey of executives dealt with their loyalty to the
company. One of the questions was, “If you were given an offer
by another company equal to or slightly better than your present
position, would you remain with the company or take the other
position?” The responses of the 200 executives in the survey
were cross-classified with their length of service with the
company. Give all results rounded to 4 decimal
places.[2+3+2+3+1+5=16pts]
LENGTH OF
SERVICE

6. LOYALTY
< 1year
1-5 years
6-10years
>10years
total
Would remain
10
30
5
75
120
Would not remain
25
15
10
30
80
total
35
45
15
105
200
a) What is the probability that randomly chosen executive is
loyal to the company?
b) What is the probability that randomly chosen executive has
more than 10 years of service OR is not loyal to the company?

7. c) What is the probability that randomly chosen executive has
less than one year of service AND is not loyal to the company?
d) Two executives are chosen randomly. What is the probability
that both would remain with the company?
e) If an event A means „length of service is more than 10
years“, name its complement A‘.
f) Are events „would remain“ and „1-5 years of service“
independent? Justify your answer numerically and draw a clear
conclusion.

8. 5. Hospital records show that of patients suffering from a
certain disease, 75% die of it. What is the probability that
Round both final results to four decimal places. State clearly
what is a success and what is a failure.
a) of 6 randomly selected patients, exactly 4 will recover?
[3pts]
b) of 5 randomly selected patients, at least one will recover?
[4pts]
_____________________________________________________
_______________________________
6. A life insurance salesman sells on the average 3 life
insurance policies per week. Calculate the probability that:
Round final results to 4 decimal places, in all calculations state
clearly value of .
0. in a given week he will sell 2 policies [3pts]

9. 0. in a given month (assuming 4 weeks month) he will sell 11
policies [3pts]
7. A large group of students took a test in Physics and the final
grades have a mean of 72 and a standard deviation of 14. If we
can approximate the distribution of these grades by a normal
distribution,
Round values of z to two decimal places, in all three parts
sketch the normal curve with given data. Results of probability
should be stated with 4 decimal places.[3x3=9pts]
1. what percent of the students scored above 85?
1. what is the probability that randomly selected student scored
between 60 and 80?

10. 1. What is dividing point (critical value) between top 5% of the
group grades and the rest?
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