During peak hours, the time between 911 calls is known to have an average value of 9 seconds and can be thought of as independent with the same distribution. Use this information and your knowledge from class to answer the following questions if you can, and if you can't, say why not.
A. What is a reasonable distribution for the waiting time between two 911 calls during peak hours? (Name the distribution, identify the parameters and provide the probabily density function).
B. Find the expected waiting time and the variance in waiting times for the next call to 911 during peak hours.
C. Find the p=0.25 of the waiting time between two 911 calls during peak hours.
D. Suppose X1 and X2 are waiting times for the next two calls to 911 on Friday at midnight (Which falls during peak hours). Find E(10+4X1 - 6X2) and var(10+4X1-6X2).
E. For staffing purposes, a call center is interested in the average waiting time between calls for the next 81 calls during peak hours. Find the probabilty that the average wait time for the next 81 calls during peak hours is less than 7 seconds.