Question

Consider a value to be significantly low if its z score less than or equal to minus2 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 22.1 and the standard deviation was 5.1. Identify the test scores that are significantly low or significantly high.

Answer 1

A score of 11.9 or less will be considered significantly low.

A score of 32.3 or more will be considered significantly high.

Explanation:

We are given the following in the question:

Mean, μ = 22.1

Standard Deviation, σ = 5.1

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) z score less than or equal to -2

`-2 = \displaystyle(x-22.1)/(5.1)\\\\x = 5.1(-2) + 22.1\\x = 11.9`

Thus, a score of 11.9 or less will be considered significantly low.

b) z score less than or equal to 2

`2 = \displaystyle(x-22.1)/(5.1)\\\\x = 5.1(2) + 22.1\\x = 32.3`

Thus, a score of 32.3 or more will be considered significantly high.