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.