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 recentyear, the mean test score was 20.8 an the standard deviation was 5.3. Identify the test scores that are significantly low or significantly high.

What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.

Test scores are not given in this problem.

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:

[tex]\mu = 20.8, \sigma = 5.3[/tex]

Significantly high:

Scores of X when Z = 2 and higher. So

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

[tex]2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = 2*5.3[/tex]

[tex]X = 31.4[/tex]

Scores of 31.4 or higher are signicantly high.

Significantly low:

Scores of X when Z = -2 and lower. So

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

[tex]-2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = -2*5.3[/tex]

[tex]X = 10.2[/tex]

Scores of 10.2 or lower are significantly low.