Question

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not​ true?

A. The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490 .
B. An SAT score of 1490 has a z-score of -0.09
C. The SAT score of 1490 is relatively better than the ACT score of 17.0.

Answer 1

The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490 .

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A. The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490.

We find the z-score for each of these options. Whichever has the higher z-score is the better grade.

ACT:

Mean 21.1, standard deviation of 4.8. Score of 17. So
`\mu = 21.1, \sigma = 4.8, X = 17`

`Z = (X - \mu)/(\sigma)`

`Z = (17 - 21.1)/(4.8)`

`Z = -0.85`

SAT:

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Score of 1490. So
`\mu = 1518, \sigma = 325, X = 1490`

`Z = (X - \mu)/(\sigma)`

`Z = (1490 - 1518)/(325)`

`Z = -0.09`

The SAT score of 1490 has the higher z-score, so this is the better score, which means that this statement is false and A. is the answer of this question.

B. An SAT score of 1490 has a z-score of -0.09

From A., this is true

C. The SAT score of 1490 is relatively better than the ACT score of 17.0.

From A., this is true.