Question

 

Will 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 the mean of 2 customers every 5 minutes. Assume that a Poisson probability distribution can be used to describe the arrival process.

a. Compute the probability that exactly 1 customer will arrive in a 5-minute period

b. Compute the probability that exactly 3 customers will arrive in a 5-minute period

c. Compute the probability that 2 or fewer customers will arrive in a 5-minute period

d. Delays are expected if more than 3 customers arrive during any a 5-minute period. What is the probability that delays will occur?

Answer 1

d) The probability that more than 3 customers will arrive in a 5-minute period is

The probability that more than 3 customers will arrive in a 5-minute period is 0.1429

ans: The probability that delays will occur is 0.1429

We will use =POISSON.DIST(x,mean,cumulative) to get this

For example, here mean=2 and  P(X=x) is obtained by =POISSON.DIST(x,2,FALSE)

P(X<=x) is obtained using =POISSON.DIST(x,2,TRUE)

Set up the following in excel

and get this