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 score was 22.5 and the standard deviation was 5.1. Identify the scores that are significantly low or significantly high.

The z-score is given by:

z-score = (x-μ) / σ

where:

x=score

μ=mean=22.5

σ=std deviation=5.1

given that the z-score is - 2, then the lowest cost will be:

-2 = (x-22.5) / 5.1

solving for x we get:

-10.2=x-22.5

x=-10.2+22.5

x=12.3

therefor the lowest score is 12.3

Given that the z-score is 2 when the score is highest, then highest score will be:

2 = (x-22.5) / 5.1

10.2=x-22.5

x=10.2+22.5

x=32.7

therefore the highest score is 32.7