EXAMPLE 5.17 Counting ATM Customers

Suppose the number of persons using an ATM in any given hour between 9 A.M. and 5 P.M. can be modeled by a Poisson distribution with . What is the probability that more than 10 persons will use the machine between 3 P.M. and 4 P.M.?

Calculating this probability requires two steps:

  1. Write as an expression involving a cumulative probability:

  2. Calculate and subtract the value from 1. Using Excel, we again employ the “POISSON.DIST()” function. However, the third argument in the function should be “1,” which tells Excel to report a cumulative probability. Thus, we put the entry of “=POISSON.DIST(10, 8.5, 1)” to obtain . Here is a summary in Excel:
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The probability that more than 10 persons will use the ATM between 3 P.M. and 4 P.M. is about 0.24. Relying on software to get the cumulative probability is much quicker and less prone to error than the method of Example 5.16 (page 268). For this case, that method would involve determining 11 probabilities and then summing their values.