Question

Significant Values. In Exercises 9-12, consider a value to be significantly low if its 2 score is less than or equal to -2 orconsider the value to be significantly high if its 2 score is greater than or equal to 2MCAT In a recent year, scores on the Medical College Admission Test (MCAT) had a mean of 25.2 and a standard deviationof 6.4. Identify the MCAT scores that are significantly low or significantly high.

Answer 1

A MCAT score that is significantly high is a score of at least 38.

A MCAT score that is significantly low is at most 12.4.

Explanation:

The z-score formula is given by:

`Z = (X - \mu)/(\sigma)`

In which
`\mu` is the mean and
`\sigma` is the standard deviation.

In this problem, we have that:

`\mu = 25.2, \sigma = 6.4`

Significantly high if it has a zscore of at least 2

`Z = (X - \mu)/(\sigma)`

`2 = (X - 25.2)/(6.4)`

`X - 25.2 = 2*6.4`

`X = 38`

A MCAT score that is significantly high is at least 38.

Significantly low if it has a score of at most - 2

`Z = (X - \mu)/(\sigma)`

`-2 = (X - 25.2)/(6.4)`

`X - 25.2 = -2*6.4`

`X = 12.4`

A MCAT score that is significantly low is at most 12.4.