According to Nielsen Media Research, the average number of hours of TV viewing by adults (18 and over) per week in the United States is 33 hours. Suppose the standard deviation is 7.9 hours and a random sample of 42 adults is taken.

a. What is the probability that the sample average is more than 36 hours?

b. What is the probability that the sample average is less than 32 hours?

c. What is the probability that the sample average is less than 29 hours? If the sample average actually is less than 29 hours, what would it mean in terms of the Nielsen Media Research figures?

d. Suppose the population standard deviation is unknown and the sample size is still 42. If 71% of all sample means are greater than 32 hours and the population mean is still 33 hours, what is the value of the population standard deviation?