According to Nielsen Media Research, the average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the standard deviation is 11.6 hours and a random sample of 41 U.S. households is taken

a.What is the probability that the sample average is more than 54 hours?

b.What is the probability that the sample average is less than 48.6 hours?

c.What is the probability that the sample average is less than 38 hours? If the sample average actually is less than 40 hours, what would it mean in terms of the Nielsen Media Research figures?

d.Suppose the population standard deviation is unknown. If 66% of all sample means are greater than 48 hours and the population mean is still 50.4 hours, what is the value of the population standard deviation?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

2. A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8. What is the probability of each of the following?

(Round all z values to 2 decimal places. Round your answers to 4 decimal places.)

a.Taking a sample of size 10 and obtaining a sample mean of 22 or more

p=

b.Taking a sample of size 4 and getting a sample mean of more than 26

p=

3.A random sample of size40is taken from a population of200members. The sample mean is64and the population standard deviation is9. Construct a 96% confidence interval to estimate the population mean. What is the point estimate of the population mean? (Round your answers to 2 decimal places.) The point estimate of the population mean is