6.10 What is wrong?Explain what is wrong in each of the following statements.

(a) The central limit theorem states that for largen, the population mean m is approximately Normal.

(b) For largen, the distribution of observed values will be approximately Normal.

(c) For sufficiently largen, the 68-95-99.7 rule says thatxshould be within m 6 2s about 95% of the time.

6.14 Total sleep time of college students.In Example 6.1 (page 289), the total sleep time per

night among college students was approximately Normally distributed with mean m 5 6.78 hours and standard deviation s 5 1.24 hours. You plan to take an SRS of sizen5 150 and compute the average total sleep time.

(a) What is the standard deviation for the average time? (b) Use the 95 part of the 68-95-99.7 rule to describe the variability of this sample mean.

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