Given that 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.
![\begin{tabular} {|c|c|} x&f(x)\\[1ex] 10&0.05\\ 20&0.10\\ 30&0.10\\ 40&0.20\\ 50&0.35\\ 60&0.20 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0Ax%26f%28x%29%5C%5C%5B1ex%5D%0A10%260.05%5C%5C%0A20%260.10%5C%5C%0A30%260.10%5C%5C%0A40%260.20%5C%5C%0A50%260.35%5C%5C%0A60%260.20%0A%5Cend%7Btabular%7D)
Part A:
Is this probability distribution
valid?
The sum of f(x) = 0.05 + 0.10 + 0.10 + 0.20 + 0.35 + 0.20 = 1
Since 0 ≤ f(x) ≤ 1, thus the distribution is a valid probability distribution.
Part B:
What is the probability MCC will obtain more
than 30 new clients (to 2 decimals)?
The probability that the MCC will obtain more than 30 new clients is given by

Part C:
What is the probability MCC will obtain
fewer than 20 new clients(to 2 decimals)?
The probability that MCC will obtain fewer than 20 new clients is given by

Part D
Compute the expected value
The expected value is given by

Part 5:
The variance is given by