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. an sat score of 1490 has a z - score of - 0.09. b. the act score of 17.0 is relatively better than the sat score of 1490. c. the sat score of 1490 is relatively better than the act score of 17.0. d. an act score of 17.0 has a z - score of - 0.85.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for SAT score of 1490

For SAT, $\mu = 1518$ and $\sigma=325$. Using the z - score formula, $z_{SAT}=\frac{1490 - 1518}{325}=\frac{- 28}{325}\approx - 0.09$. So option A is true.

Step3: Calculate z - score for ACT score of 17.0

For ACT, $\mu = 21.1$ and $\sigma = 4.8$. Using the z - score formula, $z_{ACT}=\frac{17.0 - 21.1}{4.8}=\frac{-4.1}{4.8}\approx - 0.85$. So option D is true.

Step4: Compare z - scores

The higher the z - score, the relatively better the score is. Since $z_{SAT}\approx - 0.09$ and $z_{ACT}\approx - 0.85$, and $-0.09>-0.85$, the SAT score of 1490 is relatively better than the ACT score of 17.0. So option C is true.

Step5: Analyze option B

Since the SAT score of 1490 has a higher z - score than the ACT score of 17.0, the ACT score of 17.0 is not relatively better than the SAT score of 1490. So option B is not true.

Answer:

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