Willow Brook National Bank operates a drive-up teller window that allows custome

Question

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 30 customers per hour or 0.5 customers per minute.

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

=  per six minute period

Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a six-minute period. If required, round your answers to four decimal places.

Delays are expected if more than three customers arrive during any six-minute period. What is the probability that delays will occur? If required, round your answer to four decimal places.

P(Delay Problems) = ________

x P(x) 0    1 2 3

Explanation / Answer

Arrival rate = 0.5 Customers per minute ... Given

= Customer rate per six minutes = 0.5 * 6 = 3 Customers per six minutes

This probability function follows poisson's distribution

Equation for poisson's distribution given by P(X)= [(e- * x )/ x!]

Where e = Mathematical constant = 2.71828

= 3

Substituting Values of X = 0,1,2,3

Part B

To Find P(Delay Occurs)

Delay occurs when more than 3 customer arrives

Probability of more than 3 = 1 - (Probability of 3)

= 1- (0.04978 + 0.1493 + 0.2240 + 0.2240)

=1 - 0.6471

=0.3528

Hence probability of delay occurs = 0.3528

X P(X) 0 0.04978 1 0.1493 2 0.2240 3 0.2240

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