The management at Ohio National bank doesn't want its customers to wait in line for service for too long. The manager of branch of this bank determined that the customers currently have to wait average of 8 minutes for service. Assume that the waiting times for all customers at this branch have a normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.
a) Find the probability that a randomly selected customer will have to wait for less than 3 minutes.
b) What percentage of the customers have to wait for 10 to 13 minutes?
c) What percentage of the customers have to wait for 6 to 12 minutes?
d) Is it possible that a customer may have to wait longer than 16 minutes for service?