A local super market has installed a self-service checkout counter. If X is the

Question

A local super market has installed a self-service checkout counter. If X is the number of customers who check out through self-service during a 10 minute period and we assume that the conditions of the Poisson random variable are satisfied with a mean of 6 customers per 10 minute period, what is the probability that: a. Exactly 6 customers will check out during any 10 minute period? b. No more than 5 customers will check out during any 10 minute period? c. Exactly 4 customers will check out during any 15 minute period?

Explanation / Answer

= 6 per 10 minute period

P(X = x) = e- * x / x!

a) P(X = 6) = e-6 * 66 / 6! = 0.1606

b) P(X < 5) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5)

                  = e-6 * 60 / 0! + e-6 * 61 / 1! + e-6 * 62 / 2! + e-6 * 63 / 3! + e-6 * 64 / 4! + e-6 * 65 / 5!

                  = 0.4457

c) = 9 per 15 minute

P(X = 4) = e-9 * 94 / 4! = 0.0337

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