Question

A test is used to access readiness for college. In a recent year, the mean test score was 20.7 and the standard deviation was 4.5. Identify the test scores that are significantly low or significantly high.

Answer 1

We can calculate limits required with the condition of 2 deviations from the mean and we got:

`Lower = \mu -2*\sigma = 20.7 -2*4.5 = 11.7`

If a value is lower than 11.7 we can consider it as too low

`Upper = \mu +2*\sigma = 20.7 +2*4.5 = 29.7`

If a value is Higher than 29.7 we can consider it as too high

Explanation:

For this case we know the following info:

`\mu = 20.7` represent the mean

`\sigma = 4.5`

And we want to find scores that are significantly low or significantly high

We can calculate limits required with the condition of 2 deviations from the mean and we got:

`Lower = \mu -2*\sigma = 20.7 -2*4.5 = 11.7`

If a value is lower than 11.7 we can consider it as too low

`Upper = \mu +2*\sigma = 20.7 +2*4.5 = 29.7`

If a value is higher than 29.7 we can consider it as too high