Question

The board of examiners that administers the real estate broker examination in a certain state found that the mean score on the test was 426 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80%of all applicants pass, what is the passing score? assume tht the score are normally distributed. Draw the normal curve, label and shade the area.

Answer 1

z-score for 80% to pass = -0.842.

`-0.842=(X-426)/(72)`
-60.624 = X - 426
X = 426 - 60.624
X = 365
Therefore the required passing score is 365.

Answer 2

The students scoring more than 366 will be best 80%of all applicants.

Explanation:

We are given the following information in the question:

Mean, μ = 426

Standard Deviation, σ = 72

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the value of x such that the probability is 0.2

P(X < x)

`P( X < x) = P( z < \displaystyle(x - 426)/(72))=0.2`

Calculation the value from standard normal z table, we have,

`P(z<-0.842) = 0.2`

`\displaystyle(x - 426)/(72) = -0.842\\x = 365.376 \approx 366`

Hence, the the passing score is 366 or higher. The students scoring more than 366 will be best 80%of all applicants.