A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with mean 20 minutes and standard deviation 4 minutes.

(a) What is the probability that a delivery will take between 15 and 25 minutes?

(b) The service does not charge for the pizza if delivery takes more than 30 minutes. What is the probability of getting a free pizza from a single order?

(c) During final exams week, a student plans to order pizza five consecutive evenings. Assume that these delivery times are independent of each other. What is the probabil- ity that the student will get at least one free pizza?

(d) Find the shortest range of times that includes 40% of all deliveries from this service.

(e) For a single delivery, state in which of the following ranges (expressed in minutes) delivery time is most likely to lie. 18-20 19-21 20-22 21-23

(f) For a single delivery, state in which of the following ranges (expressed in minutes) delivery time is least likely to lie. 18-20 19-21 20-22 21-23