1) The total sleep time per night among college students was approximately Normally distributed with mean = 6.7 hours and standard deviation = 1.5 hours.

1)     The total sleep time per night among college students was approximately Normally distributed with mean µ= 6.7 hours and standard deviation σ= 1.5 hours. You plan to take an SRS of size n= 225 and compute the average total sleep time. (10p)

a.     What is the standard deviation for the average time? 

b. What is the probability that your average will be below 6.9 hours?