Question

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.

Answer 1

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