Question

For the mathematics part of the SAT the mean is 514 with a standard deviation of​ 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the ACT. Use​ z-scores to determine on which test he performed better.

Answer 1

Answer:

Bob performed better in mathematics part of the SAT than the ACT

Step-by-step explanation:

We need to calculate the z-scores for both parts and compare them.

Z-score for the SAT is calculated using the formula:

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

where $\mu=514$ is the mean and $\sigma=113$ is the standard deviation, and $X=660$ is the SAT test score.

We plug in these values to obtain:

$Z=\frac{660-514}{113}$

$Z=\frac{146}{113}=1.29$ to the nearest hundredth.

We use the same formula to calculate the z-score for the ACT too.

Where $\mu=20.6$ is the mean and $\sigma=5.1$ is the standard deviation, and $X=27$ is the ACT test score.

We substitute the values to get:

$Z=\frac{27-20.6}{5.1}=1.25$ to the nearest hundredth.

Since 1.29 > 1.25, Bob performed better in mathematics part of the SAT