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West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. x f ( x ) 10 .05 20 .10 30 .10 40 .20 50 .35 60 .20 a. Is this probability distribution valid? Explain. b. What is the probability MCC will obtain more than 30 new clients? c. What is the probability MCC will obtain fewer than 20 new clients? d. Compute the expected value and variance of x .

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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Section
BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 5.3, Problem 19E
Textbook Problem
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West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.

x f(x)
10 .05
20 .10
30 .10
40 .20
50 .35
60 .20
  1. a. Is this probability distribution valid? Explain.
  2. b. What is the probability MCC will obtain more than 30 new clients?
  3. c. What is the probability MCC will obtain fewer than 20 new clients?
  4. d. Compute the expected value and variance of x.

a.

To determine

Explain whether the distribution is valid or not.

Explanation of Solution

Calculation:

The table represents the probability distribution for the number of new clients for marriage counseling for the next year.

The rules for a discrete probability distribution are,

  • The sum of the probabilities must equal to 1. That is, f(x)=1.
  • Each probability must be between 0 and 1, inclusive. That is, 0f(x)1

b.

To determine

Find the probability that the MCC will obtain more than 30 new clients.

c.

To determine

Find the probability that the MCC will obtain fewer than 20 new clients.

d.

To determine

Compute the expected value and variance of the random variable x.

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Chapter 5 Solutions

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