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.

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-07-20T08:31:12+02:00

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:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

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

We plug in these values to obtain:

[tex]Z=\frac{660-514}{113}[/tex]

[tex]Z=\frac{146}{113}=1.29[/tex] to the nearest hundredth.

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

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

We substitute the values to get:

[tex]Z=\frac{27-20.6}{5.1}=1.25[/tex] to the nearest hundredth.

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