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Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission?

Answer :

Answer:

The minimum score required for admission is 558.75.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110.

This means that [tex]\mu = 501, \sigma = 110[/tex]

A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission

This is the 100 - 30 = 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.525 = \frac{X - 501}{110}[/tex]

[tex]X - 501 = 0.525*110[/tex]

[tex]X = 558.75[/tex]

The minimum score required for admission is 558.75.

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