Question

Which score has a higher relative position, 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? A score of 688 A score of 92 Both scores have the same relative position.

Answer 1

Answer:

A score of 92

Step-by-step explanation:

The score which has higher z-score has a higher relative position,

Since, z-score or standard score of a score x is,

$z=\frac{x-\mu }{\sigma}$

Where, $\mu$ is mean,

$\sigma$ is standard deviation,

Thus,

The z-score of a score of 92 on a test with a mean of 71 and a standard deviation of 15 is,

$z_1=\frac{92-71}{15}$

$=\frac{21}{15}$

$=1.4$

Also, the z-score of a score of 688 on a test with a mean of 493 and a standard deviation of 150 is,

$z_2=\frac{688-493}{150}$

$=\frac{195}{150}$

$=1.3$

Since, $z_1>z_2$

Hence, A score of 92 has the higher relative position.

Answer 2

solution:

a score of 92 has z score of

z=\frac{x-μ}{σ}=\frac{92-71}{5}=1.40

a score of 688 has z score of

z=\frac{x-μ}{σ}=\frac{688-493}{150}=1.30

a score of 92 is better because its z score is higher