6.24 Total sleep time of college students. In Example 5.4 (page 293), the total sleep time per night among college students was approximately Normally distributed with mean μ = 6.78 hours and standard deviation σ = 1.24 hours. You initially plan to take an SRS of size n = 175 and compute the average total sleep time.

1. (a) What is the standard deviation for the average time in hours? in minutes?

2. (b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean.

3. (c) What is the probability that your average will be below 6.9 hours?