Question

For the most recent year available, the mean annual cost to attend a private university in the United States was $20,207. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,375. Use Appendix B.3. Ninety percent of all students at private universities pay less than what amount

Answer 1

Answer:

Ninety percent of all students at private universities pay less than $25,807.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 20207, \sigma = 4375$

Ninety percent of all students at private universities pay less than what amount

Less than the 90th percentile, which is X when Z has a pvalue of 0.9. So X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 20207}{4375}$

$X - 20207 = 1.28*4375$

$X = 25807$

Ninety percent of all students at private universities pay less than $25,807.