Customers arrive at a one-window drive-in bank according to a Poisson distribution, with a mean of 10 per hour. The service time per customer is exponential, with a mean of 5 minutes. There are three spaces in front of the window, including the car being served. Other arriving cars line up outside this 3-car space.

(a) What is the probability that an arriving car can enter one of the 3-car spaces?

(b) What is the probability that an arriving car will wait outside the designated 3-car space?

(c) How long is an arriving customer expected to wait before starting service?

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(d) How many car spaces should be provided in front of the window (including the car being served) so that an arriving car can find a space there at least 90% of the time?