Question

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 34 minutes and a standard deviation of 5 minutes. Using the empirical rule, determine the interval of minutes that the middle 95% of customers have to wait.

Answer 1

The interval of minutes that the middle 95% of customers have to wait is between 24 and 44 minutes.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 34 minutes, standard deviation of 5 minutes.

Interval of minutes that the middle 95% of customers have to wait.

Within 2 standard deviations of the mean. So

34 - 2*5 = 24 minutes.

34 + 2*5 = 44 minutes.

The interval of minutes that the middle 95% of customers have to wait is between 24 and 44 minutes.