Question: (10 points) A recent marketing research conducted by the American Automobiles Dealership Association has revealed that 42% of the households with an annual income between $45,000 and $58,000 have bought a new car within the past four years. In a random sample of 11 households earning between $45,000 and $58,000:

a. What is the probability that exactly 6 of these households purchased a new car during the last four years?

b. What is the probability that at least eight households purchased a new car during the last four years? List and use your formulas for this part.

c. What is the probability that at most three households purchased a new car during the last four years?