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 $20,332. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,250.

Ninety-nine percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.)

Solution

Normal Distribution
Mean ( u ) =20232
Standard Deviation ( sd )=4250
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.99
Value of z to the cumulative probability of 0.99 from normal table is 2.326
P( x-u/s.d < x - 20232/4250 ) = 0.99
That is, ( x - 20232/4250 ) = 2.33
--> x = 2.33 * 4250 + 20232 = 30117.5 ~ 30118