Response to the following problem:
Customers arrive at Pete's Coffee Shop on the average of one every 5 minutes, according to a Poisson distribution. The average time Pete spends serving a customer is 3 minutes, and the service times are believed to follow an exponential distribution.
The shop is run entirely by Pete, and customers are served on a first come, first-served basis.
a. What is the probability that exactly 2 customers will arrive at Pete's in a 15-minute period?
b. What is the probability that more than 3 customers will arrive in a 30-minute period?
c. What is the probability that the service time for a customer is under 2 minutes?
d. On the average, how long does a customer spend waiting for service at Pete's?
e. What is the probability that a customer spends less than 5 minutes at Pete's?
f. What is the average number of customers present at Pete's?
g. What percentage of Pete's time is spent serving customers?