91Ó°ÊÓ

A store serves 15 customers per hour. We need to calculate the probability that the store will serve more than 20 customers in a particular 2-hour period.

Let X be the random variable that denotes the number of customers served in 2 hours. So, we have to compute P(X>20).

The average number of customers served per hour is 15, so in a 2-hour, the average number is 30. So, X follows a Poisson distribution with parameter 30. Now,

\(\begin{array}{l}P\left( {X = x} \right) = \frac{{{\lambda ^x}}}{{x!}}{e^{ - \lambda }}\\P\left( {X > 20} \right) = \sum\limits_{i = 21}^\infty {P\left( {X = i} \right)} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sum\limits_{i = 21}^\infty {\frac{{{{30}^x}}}{{x!}}{e^{ - 30}}} \end{array}\)