# Exam P Practice Problem 28 – Wait Time to See Doctor

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Problem 28A

In the previous years, the wait time (in minutes) for a patient to see a doctor at a large medical clinic followed a distribution with the following moment generating function:

$\displaystyle M(t)=\frac{4}{4-100t} \ \ \ \ \ \ \ \ \ \ 4-100t>0$

In the current year, the administrator of the clinic still believes that the wait time to see a doctor follows the same distribution except that the mean wait time has increased by 50% (due to the fact that a higher volume of patients is being served by the same number of medical doctors).

What is the probability that in the current year the wait time for a patient to see a doctor is less than 30 minutes?

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Problem 28B
Use the same information as in Problem 28A. What is the percent increase in the variance of the wait time to see a doctor between the current year and the previous years?

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