eleanor scores 680 on the sat mathematics test. the distribution of sat scores is symmetric with a mean of…

eleanor scores 680 on the sat mathematics test. the distribution of sat scores is symmetric with a mean of 500 and a standard deviation of 100. gerald takes the act mathematics test and scores a 27. the act scores are also symmetric and have a mean of 18 and standard deviation of 6. find the z - score of each student. which student did better on their exam relative to other scores? eleanors z - score select geralds z - score select which student did better? select

eleanor scores 680 on the sat mathematics test. the distribution of sat scores is symmetric with a mean of 500 and a standard deviation of 100. gerald takes the act mathematics test and scores a 27. the act scores are also symmetric and have a mean of 18 and standard deviation of 6. find the z - score of each student. which student did better on their exam relative to other scores? eleanors z - score select geralds z - score select which student did better? select

Answer

Explanation:

Step1: Calculate Eleanor's z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Eleanor, $x = 680$, $\mu=500$, $\sigma = 100$. $z_{Eleanor}=\frac{680 - 500}{100}=\frac{180}{100}=1.8$

Step2: Calculate Gerald's z - score

For Gerald, $x = 27$, $\mu = 18$, $\sigma=6$. $z_{Gerald}=\frac{27-18}{6}=\frac{9}{6}=1.5$

Step3: Compare the z - scores

Since $1.8>1.5$, Eleanor has a higher z - score.

Answer:

Eleanor's Z - score: $1.8$; Gerald's Z - score: $1.5$; Which student did better?: Eleanor.