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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. 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.
There are an infinite number of pairs of values a and b such that P(a<Z<b)=0.8 .
The shape of the bell curve causes the distance between a and b to be minimized if we center this interval on zero (which means a=-b ).