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Assume that scores on a widely used standardized test are normally distributed with a mean of...

Assume that scores on a widely used standardized test are normally distributed with a mean of 750 and a standard deviation of 100. (Consider the distribution of scores to be a population.) If a university admits only the top 10% of the students taking the test, what is the lowest score a student can obtain and be admitted? What is the closest Z score corresponding to this value? What is the raw test score for this value?

math   Statistics-And-Probability   
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Answer #1

We need to find the z1 such that:

P(z < z1) = 0.90

This means that all scores less than z1 have 90% of the students

From the z-table, z1 = +1.28

1.28 = (X - 750)/100
X = 750 + 128 = 878

X = 878 (z-score = 1.28) is the lowest score a student can obtain and be admitted.

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