Question

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 24 minutes and a standard deviation of 5 minutes. Using the empirical rule, what percentage of customers have to wait between 19 minutes and 29 minutes?

Answer 1

To solve this problem using the empirical rule (also known as the 68-95-99.7 rule), we first need to identify how the waiting times are distributed around the mean.

Given:
- Mean (μ) = 24 minutes
- Standard deviation (σ) = 5 minutes

According to the empirical rule:
- Approximately 68% of the data falls within one standard deviation of the mean (μ ± σ).
- Approximately 95% falls within two standard deviations (μ ± 2σ).
- Approximately 99.7% falls within three standard deviations (μ ± 3σ).

We need to find the percentage of customers who have to wait between 19 minutes and 29 minutes.

1. Calculate one standard deviation below and above the mean:
- Lower bound: μ - σ = 24 - 5 = 19 minutes
- Upper bound: μ + σ = 24 + 5 = 29 minutes

This range (19 to 29 minutes) is exactly one standard deviation from the mean.

According to the empirical rule:
- About 68% of the customers have to wait between 19 minutes and 29 minutes.

Thus, the percentage of customers that wait between 19 minutes and 29 minutes is approximately **68%**.