Question

At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 12 minutes and a standard deviation of 2minutes. Using the empirical rule, determine the interval of minutes that the middle99.7% of customers have to wait.

Answer 1

By the empirical rule 99.7% of the customers fall within the interval bounded by

`\bar{x}-3\sigma\text{ and }\bar{x}+3\sigma`

In this case,

`\begin{gathered} \bar{x}=12\min \text{ and} \\ \sigma=2\min \end{gathered}`

Therefore,

`\begin{gathered} \bar{x}-3\sigma=12-3(2)=12-6=6\min s \\ \bar{x}+3\sigma=12+3(2)=12+6=18\min s \end{gathered}`

Hence, the interval of minutes that the middle 99.7% of customers have to wait is given by

(6mins, 18mins)