Question

Suppose SAT critical reading scores are normally distributed with a mean of 404 and a standard deviation of 84. A university plans to recruit students whose scores are in the 90th percentile. What is the minimum score required for recruitment?

Answer 1

Answer

Minimumscore required for therecruitment

Explanation

For a normal distribution, it is quite important to explain what it means to normalize the required score.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ

z = standardized score of the minimum score required to be in the 90th percentile

x = minimum required score to be in the 90th percentile

μ = mean of the distribution = 404

σ = standard deviation of the distribution = 84

The minimum score required to be in the 90th percentile will be the score that is greater than 90% of all the scores.

P(Z ≤ z) = 0.90

From the tables,

z = 1.282

z = (x - μ)/σ

z = 1.282

x = ?

μ = mean of the distribution = 404

σ = standard deviation of the distribution = 84

1.282 = (x - 404)/84

x - 404 = (84) (1.282)

x - 404 = 107.688

x = 404 + 107.688

x = 511.688 = 511.7

Hope this Helps!!!