Question

7. 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 450 and the standard deviation was 75. If the board wants to set the passing score so that only the best 12% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. Round to the nearest whole number.

Answer 1

Given that,

mean = = 450

standard deviation = = 75

Using standard normal table,

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z ) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 1.18 ) = 0.88  

z = 1.18 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.18*75+450

x= 538.5

x=539