8. You are in charge of advertising for the company which produces car vacuum cleaners and management is after you to improve sales. You are advertising on TV in the 9-10 PM. slot. For the past year, you have collected information about all purchasers of you car vacs via a warranty registration questionnaire. From this, you know that 10,000 viewers of your commercial bought a car vac. Of these 10,000 buyers, the following per centages fell into each viewer type category: Relative Frequency (i) Children and teenagers 0.01 (ii) Males 20-35 0.35 (iii) Females 20-35 0.55 (iv) People over 35 0.09 You have talked to a friend Who works for the Nielsen rating company and are rea sonably condent that the following numbers of people viewed your commercial dur- ing the past year: Absolute Frequency (i) Children and teenagers 50,000 (ii) Males 20-35 6,000 (iii) Females 20-35 14,000 (iv) People over 35 30,000 3 Given all the information you have collected you want to know whether you should direct your advertising towards male or female viewers. Most purchasers are young adult females. However, that could be because they are more responsive to your adver- tising, or simply because they watch more television. In order to decide this issue: (a) Calculate the marginal probabilities (A viewer buys or not, type of viewer) (b) Using Bayes Theorem, what are the probabilities that viewers of each type who see the commercial will buy a car vac? Do you think that you should redirect your commercial to appear during the sports programs? Why or why not? Other ideas? (c) Construct a joint probability table