West Virginia has one of the highest divorce rates in the na

West Virginia has one of the highest divorce rates in the nation with an annual rate of approximately 5 divorces per 100 people. The Marital counseling center, inc. (MCC) thinks that he 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.

A) is the 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.

Solution

A) is the probability distribution valid? explain.

Yes, becuase sum of all f(x)=1

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B) what is the probability MCC will obtain more than 30 new clients?

P(X>30) = P(X=40)+P(X=50)+P(X=60)

=0.2+0.35+0.2

=0.75

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C) what is the probability MCC will obtain fewer than 20 new clients?

P(X<20) =P(X=10)=0.05

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D) compute the expected value and variance of x.

E(X)=expected value =sum of x*f(x)

=10*0.05+20*0.1+30*0.1+40*0.2+50*0.35+60*0.2

=43

E(X^2)=expected value =sum of x^2*f(x)

=10^2*0.05+20^2*0.1+30^2*0.1+40^2*0.2+50^2*0.35+60^2*0.2

=2050

Variance= E(X^2) -[E(X)]^2

=2050-43^2

=201