Question

For the most recent year available, the mean annual cost to attend a private university in the United States was $20,107. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,475.

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

Answer 1

Answer:

Given ,

To determine the z value,

Here we have to use the standard normal distribution table which is used to separate the top 1%

from the 99%

P(z > 2.33) = .0099 [since from z table]

let us consider,

z = (x-µ)/s --------->(1)

where as

z = 2.33

mean = 20107

standard deviation = 4475

Now substitute all these values in eq(1)

z = 2.33 = (x-20107)/4475

x = 2.33*4475 + 20107

x = 30533.75

Hence ninety-nine percent of all students at private universities pay less than 30,534.