At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 18 minutes and a standard deviation of 3 minutes. Using the empirical rule, what percentage of customers have to wait between 12 minutes and 24 minutes?

Answer 1

To calculate the percentage of customers who have to wait between 12 and 24 minutes using the empirical rule, we need to find the z-scores corresponding to 12 and 24 minutes and then calculate the area under the normal curve between these two z-scores.

First, we calculate the z-score for 12 minutes:

z = (X - μ) / σ
z = (12 - 18) / 3
z = -2

Next, we calculate the z-score for 24 minutes:

z = (X - μ) / σ
z = (24 - 18) / 3
z = 2

By using the empirical rule, we know that approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

Since the range of 12 to 24 minutes falls within 2 standard deviations of the mean, we can conclude that approximately 95% of customers have to wait between 12 and 24 minutes for their food.