Respuesta :
Answer:
95% of all students at private universities pay less than $58,302.5.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Mean of $50,900, standard deviation of $4,500
This means that [tex]\mu = 50900, \sigma = 4500[/tex]
Ninety-five percent of all students at private universities pay less than what amount?
Pay less than the 95th percentile, and the amount is given by X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 50900}{4500}[/tex]
[tex]X - 50900 = 1.645*4500[/tex]
[tex]X = 58302.5[/tex]
95% of all students at private universities pay less than $58,302.5.
