Question

The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 553 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed

Answer 1

Answer:

The passing score is 645.2

Step-by-step explanation:

Problems of normally distributed samples are solved using 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 problem, we have that:

$\mu = 553, \sigma = 72$

If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28.

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

$1.28 = \frac{X - 553}{72}$

$X - 553 = 1.28*72$

$X = 645.2$

The passing score is 645.2