A bank manager wishes to provide prompt service for customers at the bank's drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period. Let x denote... the number of customers arriving per 15-minute period.
Assuming x has a Poisson distribution:
(a) Find the probability that 10 customers will arrive in a particular 15-minute period.
(b) Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.
(c) Find the probability that there will be a significant delay at the drive-up window. That is, find the probability that more than 10 customers will arrive during a particular 15-minute period.