Customer Arrival Time Analysis Using Poisson Distribution

Customers arrive to the company at a rate, on average, of
one per hour with a Poisson distribution. The company is staffed by a single
individual(the owner) who takes on average 30 minutes with each customer with a
standard deviation of 15
minutes.

a. The owner would like the average wait time to be at most
around 10 minutes. How much time can he spend with each customer, on
average, to meet this goal? Assume the standard deviation of the service time
is still 15 minutes.

b. On average, how many customers are in the agency at any
time?

c. What percent of the time does the owner spend with
customers?

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