SOLUTION: According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) stan

Question 1071056: According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) standard deviation is known to be 11.8 hours. A random sample of 42 U.S. households is taken. (Hint: Review the central limit theorem about sampling distributions)
a. What is the probability that the sample mean is more than 52 hours?
b. What is the probability that the sample mean is less than 47.5 hours?
c. What is the probability that the sample mean is less than 40 hours?
d. Assume that the sample mean actually is less than 40 hours. What does this mean about the Nielsen Media Research figures that claim the population mean is 50.4 hours? Explain.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sigma/sqrt(n)
> (52-50.4)/11.8/sqrt(42)=1.6/1.82=0.1898
probability is 0.1898
---------------------
< (47.5-50.4)/11.8/sqrt(42)=less than -2.9/1.821 or < z of -1.592
Probability is 0.0557
--------------------
<-10.4/1.821 or z< -5.711
This is <<0.0001
If that is the case, then the claim is not likely to be true.
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