5.22 It is known that amounts of money spent on clothing in a year by students on a particular campus follow a normal distribution with a mean of $380 and a standard deviation of $50.

a. What is the probability that a randomly chosen student will spend less than $400 on clothing in a year?

b. What is the probability that a randomly chosen student will spend more than $360 on clothing in a year?

c. Draw a graph to illustrate why the answers to parts

(a) and

(b) are the same.

d. What is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?

e. Compute a range of yearly clothing expenditures—
measured in dollars—that includes 80% of all students on this campus? Explain why any number of such ranges could be found, and find the shortest one.