The Nielsen Media Group is the major media ratings company and conducts surveys on a weekly basis to determine household viewing choices. The following table shows the top 10 broadcast television programs for the week of September 29, 2008.

Rank* Program Network Rating** Viewers***
1 Dancing with the Stars ABC 12.2 18.883 2 NCIS CBS 11 17.47 3 60 Minutes CBS 10.5 16.648 4 Dancing W/Stars Results ABC 10.2 15.491 5 Desperate Housewives ABC 10 15.685 6 Mentalist, The CBS 9.8 15.484 7 CSI: NY CBS 9.6 14.878 8 Criminal Minds CBS 9.5 14.78 9 CSI: Miami CBS 9.2 14.345 10 NBC Sunday Night Football

a. Suppose that the producers of NCIS commissioned a study that called for the consultants to randomly call 25 people immediately after the NCIS time slot and interview those who said that they had just watched NCIS. Suppose the consultant submits a report saying that it found no one in the sample of 25 homes who claimed to have watched the program and therefore did not do any surveys. What is the probability of this happening, assuming that the Nielsen ratings for the show are accurate?

b. Assume the producers for Desperate Housewives planned to survey 1,000 people on the day following the broadcast of the program. The purpose of the survey was to determine what the reaction would be if one of the leading characters was murdered on the show. Based on the Nielsen ratings, what would be the expected number of people who would end up being included in the analysis, assuming that all 1,000 people could be reached?