Statistics 19. W est Virgin approximately 5 divorces per 1000 people (Centers fo

Question

Statistics

19. W est Virgin approximately 5 divorces per 1000 people (Centers for Disease Control and Preventiorn 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 distributio for x = the number of new clients for marriage counseling for the next year. ia has one of the highest divorce rates in the nation with an annual rate of f(x) 05 10 .10 .20 .35 .20 10 50 60 a. Is this probability distribution valid? Explain. What is the probability MCC will obtain more than 30 new clients? What is the probability MCC will obtain fewer than 20 new clients? Compute the expected value and variance of x. b. c. d. The nrobahility distribution for damage claims paid by the Newton Automobile Insurance 20

Explanation / Answer

a) Probability distribution is valid, because the sum of probabilities is equal to 1

b) Probability that MCC will obtain more than 30 new clients = 0.2+0.35+0.2 = 0.75

this is the sum of probability corresponding to x=40,50,60

c) Probability that MCC will obtain less than 20 new clients = 0.05

this is the probability corresponding to x=10

d) Expected value of x = 10*0.05+20*0.1+30*0.1+40*0.2+50*0.35+60*0.2 = 43

Variance = 0.05*(10-43)2 + 0.10*(20-43)2 + 0.10*(30-43)2 + 0.20*(40-43)2 + 0.35*(50-43)2 + 0.20*(60-43)2 = 201

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