Problem $3-17($Algo$)$

You are the manager of Spartan Care $-$ a local Redi$-$Care facility. While this facility serves a range of clients, everyone agrees that quick service is very important $($defined as the difference from the time that they arrive and are registered at the front desk until they are seen either by a nurse or a doctor$).$ Currently, you have been receiving numerous complaints from the clients that the time spent waiting to see someone is simply too long. To assess the situation, you collect the following information from a two$-$week period:

Average process utilization: $75$ percent

Average processing time: $13$ minutes

Average arrival time: $8$ minutes

Standard deviation of the processing time: $16\mathrm{.}5$ minutes

Standard deviation of the arrival time: $15\mathrm{.}0$ minutes

a$.$ What is the average wait time?

Note: Round your intermediate calculations to at least four decimal places. Round your final answer to $2$ decimal places.

Average waiting time

minutes