6.1.2 Exam: Semester 2 Exam Question 12 of 40 Suppose the commute times for employees of a large company follow a normal distribution. If the mean time is 18 minutes and the standard deviation is 5 minutes, \( 95 \% \) of the employees will have a travel time within which range? A. 13 minutes to 23 minutes B. 3 minutes to 33 minutes C. 13.25 minutes to 22.75 minutes D. 8 minutes to 28 minutes 1

To determine the range within which \( 95\% \) of the employees' commute times fall, we can use the properties of the normal distribution. Given: - **Mean (\( \mu \))** = 18 minutes - **Standard deviation (\( \sigma \))** = 5 minutes For a normal distribution: - Approximately **68%** of the data falls within \( \mu \pm 1\sigma \). - Approximately **95%** of the data falls within \( \mu \pm 1.96\sigma \). - Approximately **99.7%** of the data falls within \( \mu \pm 3\sigma \). Calculating the \( 95\% \) range: \[ \mu \pm 1.96\sigma = 18 \pm (1.96 \times 5) = 18 \pm 9.8 \] This results in: \[ 18 - 9.8 = 8.2 \text{ minutes} \] \[ 18 + 9.8 = 27.8 \text{ minutes} \] So, the \( 95\% \) range is approximately **8.2 minutes to 27.8 minutes**. **Among the provided options, the closest range is:** **D. 8 minutes to 28 minutes** **Answer:** **D. 8 minutes to 28 minutes**