Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly high if its z score is greater than or equal to 2. A test is used to assess readiness for college. In a recent year, the mean test score was 20.620.6 and the standard deviation was 5.25.2. Identify the test scores that are significantly low or significantly high.

Test scores of 10.2 or lower are significantly low.

Test scores of 31 or higher are significantly high

Step-by-step explanation:

Z-score:

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:

Significantly low:

Z-scores of -2 or lower

So scores of X when Z = -2 or lower

Test scores of 10.2 or lower are significantly low.

Significantly high:

Z-scores of 2 or higher

So scores of X when Z = 2 or higher

Test scores of 31 or higher are significantly high

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