Floyd’s Barber Shop has one barber chair and seven chairs for waiting customers. If the place is full, customers go elsewhere. Arrivals occur according to a Poisson distribution with mean four per hour. The time to get a haircut is exponential with mean 15 minutes. Determine the following:

a.    The fraction of time that the barber is idle.

b.   The expected number of customers in the shop     

c.    The probability that customers will go elsewhere because the shop is full.