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 2 minutes. Using the empirical rule, what percentage of customers have to wait between 26 minutes and 38 minutes?

To determine the percentage of customers who wait between 26 minutes and 38 minutes for their food, we'll apply the **Empirical Rule** (also known as the **68-95-99.7 rule**) for normally distributed data. ### Given: - **Mean (μ):** 32 minutes - **Standard Deviation (σ):** 2 minutes ### Steps: 1. **Calculate the Z-scores:** - **Lower Limit (26 minutes):** \[ Z = \frac{26 - 32}{2} = \frac{-6}{2} = -3 \] - **Upper Limit (38 minutes):** \[ Z = \frac{38 - 32}{2} = \frac{6}{2} = 3 \] 2. **Apply the Empirical Rule:** - The Empirical Rule states that: - **68%** of the data falls within **±1σ**. - **95%** within **±2σ**. - **99.7%** within **±3σ**. 3. **Interpretation:** - Since both 26 minutes and 38 minutes are **±3σ** from the mean, approximately **99.7%** of the customers will have wait times within this range. ### **Conclusion:** **About 99.7 % of customers wait between 26 and 38 minutes.**