Answer to Question #216529 in Statistics and Probability for aasa

Question

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. Ninety-five percent of all

students at private universities pay less than what amount?

Answer 1

Let $X=$ annual cost: $X\sim N(\mu, \sigma^2).$

Given $\mu=26889, \sigma=4500.$

$$P(X<\dfrac{x-26889}{4500})=0.95$$

$$\dfrac{x-26889}{4500}=1.6449$$

$$x=4500(1.6449)+26889$$

$$x=\$34291$$

Ninety-five percent of all students at private universities pay less than $34,291.