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 546 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, to the nearest hundredth? Assume that the scores are normally distributed.

Answer 1

• 638.16

Explanation:

90% mark from z-score table is:

• z = 1.28

We have also:

• μ = 546 and
• σ = 72

According formula for z-score:

• z = (x - μ)/σ

Substitute values and solve for x:

• 1.28 = (x - 546)/72
• x - 546 = 1.28*72
• x - 546 = 92.16
• x = 92.16 + 546
• x = 638.16