Question

scores on the sat test have a mean of 1475 and a standard deviation of 286. scores on the act test have a mean of 19.7 and a standard deviation of 4.2. jamie took both tests and wonders which is relatively better: a score of 763 on the sat test or a score of 9 on the act test? (round the answers to 2 decimals.)
jamies z - score on sat is
and jamies z - score on act is
since jamies z - score on sat is select an answer z - score on act, we conclude that select an answer

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

For the SAT, $\mu = 1475$, $\sigma=286$, and $x = 763$. Then $z_{SAT}=\frac{763 - 1475}{286}=\frac{-712}{286}\approx - 2.49$.

Step3: Calculate z - score for ACT

For the ACT, $\mu = 19.7$, $\sigma = 4.2$, and $x = 9$. Then $z_{ACT}=\frac{9 - 19.7}{4.2}=\frac{-10.7}{4.2}\approx - 2.55$.

Step4: Compare z - scores

Since $-2.49>-2.55$ (i.e., $z_{SAT}>z_{ACT}$), the SAT score is relatively better.

Answer:

Jamie's z - score on SAT is $-2.49$ and Jamie's z - score on ACT is $-2.55$. Since Jamie's z - score on SAT is greater than z - score on ACT, we conclude that the SAT score is relatively better.