West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1,000 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 for x = the number of 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 valid because for x = 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?
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1,000 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 for x = the number of 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 valid because for x = 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?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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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 1,000 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 for x = the number of 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 valid because for
f(x) = .
x = 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 of x.
expected value of x=variance of x=
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