Probability - Topic 2 – Suggested Problems

1. Problem 2.4 in Barnes

2. Problem 2.26 in Barnes

3. Problem 2.40 in Barnes

4. A personnel manager has cross-classified the 400 employees of a firm according to their record of absenteeism last year and according to whether or not they were smokers, as shown in the accompanying table One of these employees is selected at random.

Number of days absent	Smoker	Nonsmoker
Less than 10	34	260
10 or more	78	28

1. What is the probability that the employee selected was a nonsmoker?
2. What is the probability that the employee selected was absent for 10 or more days?
3. Are the events "nonsmoker" and "absent less than 10 days" mutually exclusive? Explain.
4. Determine whether an employee's being absent for 10 or more days last year was independent of the employee's being a smoker.

A < 10 Absences

B > 10 Absences

C = Smoker

D = Non-Smoker

a) P(D) = 288/400 = .72

b) P(B) = 106/400 = .265

c) No, 260 employees belong to both events

d) Not indepenent

5. A mutual fund saleswoman has arranged to call upon three households tomorrow. Based on past experience, she feels that there is a 20% chance of closing a sale on each call and that the outcome of each call is independent of the others. Let X represent the number of sales she closes tomorrow.

1. Find the probability distribution of X.
2. Express the probability distribution of X graphically
3. What is the probability that more than one sale will be closed tomorrow?

a) Binomial where n = 3, p = .2 and x = number of sales

X	0	1	2	3
P(X)	.512	.384	.096	.008

b)

c) P(X>1) = P(X=2) + P(X=3)

P(X>1) = .096 + .008 = .104

6. Let X represent the number of times a student visits a nearby pizza parlor in a 1 month period. Assume that the following table is the probability distribution of X.

x	0	1	2	3
p(x)	.1	.3	.4	.2

1. Find the mean and the standard deviation of this distribution.
2. What is the probability that the student visits the pizza parlor at least twice in a month?
3. Find p(X GTE 1.5)

s = .9

b) P(X>2) = .4 + .2 = .6

c) P(X>1.5) = .4 + .2 = .6

7. In order to examine the effectiveness of its four annual advertising promotions, a mail-order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that otherwise would not have been made. The following table summarizes the data received, where the random variable X is the number of promotions indicated in the customer's responses.

x	0	1	2	3	4
p(x)	.10	.25	.40	.20	.05

1. Assuming that the responses received were accurate evaluations of individual effectiveness and that customer behavior in the coming year will not change, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
2. What is the variance of X?

a)

b)

s = 1.027