Question

Determine which score corresponds to the higher relative position. Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

Answer 1

Answer:

The score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.

Step-by-step explanation:

To find which score corresponds to the higher relative position, we find the Z-score of each score.

The z-score, which measures how many standard deviation a measure is above or below the mean, is given by the following formula:

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

In which X is the score, $\mu$ is the mean and $\sigma$ is the standard deviation.

A score of 92 on a test with a mean of 71 and a standard deviation of 15.

So $X = 92, \mu = 71, \sigma = 15$

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

$Z = \frac{92 - 71}{15}$

$Z = 1.4$

A score of 688 on a test with a mean of 493 and a standard deviation of 150.

So $X = 688, \mu = 493, \sigma = 150$

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

$Z = \frac{688 - 493}{150}$

$Z = 1.3$

Which is better?

Due to the higher z-score, the score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.