Question

Suppose that the number of customers ordering take-out at a small restaurant is a Poisson process with rate α = 4.0 customers per hour.

Answer the following questions. If necessary, round your answer to four decimal places.

(a) Find the probability that there would be at least two customers in a 450-minute period.

(b) The cashier in charge of take-outs wishes to take a 35 - minute break starting right after serving a customer. What is the probability that there will be no angry customer waiting to be served when the cashier returns from the break? Assume no customer will leave until they are served.

Answer 1

(a)

For 450 minute period,

α = 4.0 customers per hour. = 4.0 customers per 60 minutes = (4 * 450 / 60) per 450-minutes

= 30 per 450-minutes

X ~ Poisson(α = 30)

P(X 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.0000 - 0.0000

= 1

b)

For 35 minute period,

α = 4.0 customers per hour. = 4.0 customers per 60 minutes = (4 * 35 / 60) per 35-minutes

= 2.33 per 35-minutes

X ~ Poisson(α = 2.33)

Probability that there will be no angry customer waiting to be served = Probability that there will be no customer in 35 minutes period = P(X = 0) =

= 0.0973

= 1