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

Answer:

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.

Step-by-step explanation:

The z-score formula is given by:

$Z = \frac{X - \mu}{\sigma}$

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

$Z = \frac{X - \mu}{\sigma}$

$2 = \frac{X - 25.2}{6.4}$

$X - 25.2 = 2*6.4$

$X = 38$

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

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

$Z = \frac{X - \mu}{\sigma}$

$-2 = \frac{X - 25.2}{6.4}$

$X - 25.2 = -2*6.4$

$X = 12.4$

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