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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Test results At a major university, exam scores, x, in a large enrollment course are normally distributed with a mean score of 78 and standard deviation of 6. If the test is curved so that the top 10% of scores get a grade of A, find the minimum score to receive an A.

To determine

To calculate: The minimum score to receive grade A if test results at a major university, exam scores x in a large enrollment course are normally distributed with a mean score of 78 and standard deviation of 6. If the test is curved so that the top 10% of scores get a grade of A.

Explanation

Given Information:

The test results at a major university, exam scores x in a large enrollment course are normally distributed with a mean score of 78 and standard deviation of 6. If the test is curved so that the top 10% of scores get a grade of A.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

Consider that the university exam scores are normally distributed and the mean and standard deviation are as follows,

μ=78σ=6

Now the condition is if the test is curved so that the top 10% of scores get a grade of A, one has to find the minimum score to receive an A.

That is the probability condition is;

Pr(zxμσ)=0

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