West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately5 divorcesper1,000 people.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 forx= the numberof new clients for marriage counseling for the next year.

x f(x)

10 0.05

20 0.15

30 0.15

40 0.20

50 0.30

60 0.15(a)

Is this probability distribution valid? Explain.

This probability distribution

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is

is not

valid because

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f(x) 0

10 f(x) 60

1 f(x) 1

f(x) 0

forx= 10, 20, 30, 40, 50, 60.

Also,f(x) =.

(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 ofx.

expected value ofx=variance ofx=