Willow brook national bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. on weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.

There are two question related to the above information is;

1) What is the mean or expected number of customers that will arrive in a five-minute period?

Answer:

to calculate the mean, customers per minute is equal to 0.4

mean for that will arrive in a five minute period = 0.4 x 5 = 2

thus, the answer is 2.

2) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (1) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.

Given X Poisson (Mean = 2 in 5 minutes)

P (X=x) = (2^x) x exp (-2) / x!

P (X=0) = (2^0) x Exp (-2) / 1! = 0.1353353

P (X=1) = (2^1) x Exp (-2) / 1! = 0.2706706

P (X=2) = (2^2) x Exp (-2) / 2! = 0.2706706

P (X=3) = (2^3) x Exp (-2) / 3! = 0.180447