A particular program, say, program A, previously drew 30% of the television audience. To determine if a recent rescheduling of the programs on a competing channel has adversely affected the audience of program A, a random sample of 400 viewers are asked whether or not they currently watch this program.
(a) If the percentage of viewers watching program A has not changed, what is the probability that fewer than 103 out of a sample of 400 will be found to watch the program?
(b) If the number of viewers of the program is actually found to be less than 103, will this strongly support the suspicion that the population percentage has dropped? Use your calculation from part (a).