According to Canadian Radio-television and Telecommunications Commission, the average number of hours of TV viewing among adults is 27 hours per week.4 Suppose the standard deviation is 6.7 hours and a random sample of 42 Canadian households is taken.

a. What is the probability that the sample average is more than 29 hours?
b. What is the probability that the sample average is less than 23 hours?
c. What is the probability that the sample average is less than 20 hours? If the sample average actually is less than 20 hours, what would it mean in this context?
d. Suppose the population standard deviation is unknown and the sample size is still 42. If 71% of all sample means are greater than 26 hours and the population mean is still 27 hours, what is the value of the population standard deviation?