Question:

The automobile company Toyota wants to learn about five specific car models they offer in the last six months. The percent of new cars sold in the last six months and the cost for each of the models is shown in the table below. Only customers who bought one of these five models are included in the table. Car Model Rav 4 Camry Corolla Highlander Tacoma Cost $26250 $25045 $20025 $35085 $26400 Percent 138% 32% 28% 1% 1% (a) If you selected a random owner of one of these five vehicles in the last six months, what is the expected price they had to pay? What is the standard deviation? Toyota wants to learn about customer satisfaction among the owners of these five models in the last six months. They want to gather a sample of owners and they are deciding on a sampling method. Assume each owner selected is independent since they are sampling from such a large population. (b) When selecting a simple random sample of 1000 new car owners of these 5 models in the last six months, how likely is it that strictly less than 10 owners will have bought a Tacoma? (c) Toyota is concerned that the Tacoma owners will be underrepresented in a simple random sample. Briefly describe a sampling method for randomly selecting 1000 owners that will ensure 10 owners for the Tacoma and be representative of all owners of these five models in the last six months