For the most recent year available the mean annual cost to a

For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.

Solution

We require P(X < x) = 0.95

i.e. P(Z < (x - 26,889)/4,500) = 0.95

From normal tables we get:

(x - 26,889)/4,500 = 1.645

so, x = 26,889 + 1.645(4,500) => 34,291.50

Hence, 95% of students will pay less than $34,291.50