A large urban police department's CSI unit laboratory has $20$ identical, very accurate and very expensive scanning electron microscopes available for use by its crime scene investigators. Assume crimes are distributed evenly over the day in this city and, on average, an investigator requests a microscope once every four hours with a standard deviation of $4$ hours. Also, on average, he or she uses the microscope for $2$ days with a standard deviation of $1$ day. Finally, assume that CSI agents work around the clock $(24$ hours a day$),$ until the crime they are working on is solved.

a$)$ What is the average percentage of the $20$ microscopes that are being used on any given day?

b$)$ What is the average wait time a CSI analyst has to endure before getting his or her hands on a microscope to solve a super hot crime that the mayor wants solved immediately?