Question: Question 1

A network television department that sells commercial time to advertisers claims the number of homes reached per afternoon by a certain weekday soap opera has a mean of 4.5 million homes with a standard deviation of .5 million. It is known that the number of homes reached per afternoon by this program has a normal distribution, answer the following questions:

a) Assuming the department's claim is true, for what fraction of the weekday afternoons does this program reach fewer than 3.5 million homes?

b) For what fraction of weekday afternoons does this program reach between 3.1 and 5.6 million homes?

c) If the department's claim is correct, what is the probability that on two randomly selected weekday afternoons this program will reach fewer than 3.5 million homes on both days?

d) A television rating service randomly selects two weekday afternoons and finds 3.2 and 3.4 million homes, respectively, were reached by this program on the two days. Using these findings and your answer to part c, what can be said about the television department's claim?