Question 2 (20 marks)

You are the manager of a car rental company. You are preparing an annual report about the travelling distance and the rental cost of the rented cars in the daily rental department. According to the record, the daily travelling distance of a rented car follows a normal distribution with mean 40 km and standard deviation 8 km. The daily rental cost of a car is calculated as $3 per km of the traveling distance plus an additional service charge of $30.

(a) What is the probability that the travelling distance of a rented car in a day is more than 50 km?

(b) There is 33% chance that the travelling distance of a rented car in a day is less than D km. What is the value of D?

(c) Find the mean and standard deviation of the daily rental cost. (d) The senior manager suggests a promotion that fix the maximum daily rental cost at $200. Suppose there is no change in the distribution of the travelling distance due to this promotion. What percentage of daily car rents would be benefit by this promotion?