Question

question 13 of 28
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. 8 minutes to 28 minutes
d. 13.25 minutes to 22.75 minutes

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal distribution, about 95% of the data lies within \( \mu\pm2\sigma\) where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Calculate the lower and upper bounds

Given \(\mu = 18\) (mean) and \(\sigma=5\) (standard deviation).
The lower bound is \( \mu - 2\sigma=18-2\times5\).

$$18 - 10=8$$

The upper bound is \( \mu + 2\sigma=18 + 2\times5\).

$$18+10 = 28$$

Answer:

C. 8 minutes to 28 minutes