At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 32 minutes and a standard deviation of 3 minutes. Using the empirical rule, determine the interval of minutes that the middle $99.7 \%$ of customers have to wait.

Step 1 ：At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of \(32\) minutes and a standard deviation of \(3\) minutes. Using the empirical rule, determine the interval of minutes that the middle \(99.7 \%\) of customers have to wait.

Step 2 ：Since we want the middle \(99.7\%\), we need to find the interval that is \(3\) standard deviations away from the mean.

Step 3 ：mean = \(32\)

Step 4 ：std_dev = \(3\)

Step 5 ：lower_bound = mean - 3 * std_dev = \(32 - 3 * 3 = 23\)

Step 6 ：upper_bound = mean + 3 * std_dev = \(32 + 3 * 3 = 41\)

Step 7 ：\(\boxed{\text{The middle 99.7\% of customers have to wait between 23 and 41 minutes.}}\)