Question
Asked Nov 24, 2019
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The board of examiners that administers the real estate broker’s examination in a certain state found that the mean score of the test was 435 and the standard deviation was 72.  Assume that the scores are normally distributed.

a. If the board wants to set the passing score so that only the best 30% of all applicants pass, what is the passing score?

b. What are the minimum and maximum scores of the middle 75% of persons that take the exam?

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Expert Answer

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Step 1

Let X be the random variable that represents the scores .It is given that X follows normal distribution with mean = 435 and standard deviation = 72.

(a)

It is required to find the value of x1 and P(X > x1) = 0.30.

The value of x1 can be calculated as follows

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X-u P(X>x) P =0.30 =1-P Z P Z> 0.30 PZ< = 1-0.30 0.70

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Step 2

In the standard normal table, the z-value corresponding to the probability 0.70 is +0.524. Thus, 

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P(Z <0.524)=0.70

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Step 3

So, the passing scores in examina...

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=μ+:σ =435+(0.524x 72) =472.728

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