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Customer Arrival Time Analysis Using Poisson Distribution

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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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Customer arrival average rate is analyzed with a Poisson distribution.

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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 ...

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