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

Answer:

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

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

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 22.1

Standard Deviation, σ = 5.1

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a)  z score less than or equal to -2

$-2 = \displaystyle\frac{x-22.1}{5.1}\\\\x = 5.1(-2) + 22.1\\x = 11.9$

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

b)  z score less than or equal to 2

$2 = \displaystyle\frac{x-22.1}{5.1}\\\\x = 5.1(2) + 22.1\\x = 32.3$

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