Suppose ACT Composite scores are normally distributed with a mean of 20.6 and a standard deviation of 5.2. A university plans to admit students whose scores are in the top 40%. What is the minimum score required for admission? Round your answer to the nearest tenth, if necessary.

The minimum score required for admission is 21.9.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

In this problem, we have that:

A university plans to admit students whose scores are in the top 40%. What is the minimum score required for admission?

Top 40%, so at least 100-40 = 60th percentile. The 60th percentile is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.255. So

The minimum score required for admission is 21.9.

step-by-step explanation: