On the basis of past data, the owner or an automobile dealership finds that, on average 8.5 cars are sold per day on Saturdays and Sundays during the months of January and February, with the sales rate relatively stable throughout the day. Moreover, purchases appear to be independent of one another. The dealership is open 10 hours per day on each of these days. There is no reason to believe that the sales for the upcomming year will be any different from the past. a. On the first Saturday in February, the dealership will open 9am. Find the prbability that the time until the first sale is more than two hours, Pe ( T >= 2hours | m = 8.5 cars per 10 hours).
b. Find the probability that the number of sales before 11am is equal to zero, Pp (X=0 in 2 hours | m = 8.5 cars per 10 hours). Compare your answer with that from part a above - can you explain why the answers are the same?
c. The owner of the dealership gives her salespeople bonuses, depending on the total number of cars sold. She gives them $20 whenever exactly 13 cars are sold on a given day, $30 whenever 14 cars are sold, $50 whenever 15 cars sold, and $70 whenever 16 or more are sold. On any given Saturday or Sunday in Janurary or February, what is the expected bonus that the dealer will have to pay?
d. Consider the bonus scheme presented in parrt c. above. February contains exactly four Saturdays and four Sundays. What is the probality that the owner will have to pay the $20 bonuses exactly twice on those days?