Question 46 (page 181) DI, Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45% of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10. a) Develop a probability distribution for the number of students in the sample who watch soap operas. b) Find the mean and the standard deviation of this distribution. c) What is the probability of finding exactly four students who watch soap operas? d) What is the probability less than half of the students selected watch soap operas? Question 56 (page 182) According to sales information in the first quarter of 2016, 2.7% of new vehicles sold in the United States were hybrids. This is down from 3.3% for the same period a year earlier. An analyst's review of the data indicates that the reasons for the sales decline include the low price of gasoline and the higher price of a hybrid compared to similar vehicles. Let's assume these statistics remain the same for 2017. That is, 2.7% of new car sales are hybrids in the first quarter of 2017. For a sample of 40 vehicles sold in the Richmond, Virginia, area: a) How many vehicles would you expect to be hybrid? b) Use the Poisson distribution to find the probability that five of the sales were hybrid vehicles. c) Use the binomial distribution to find the probability that five of the sales were hybrid vehicles.