Question

jayden scored 67 in the class with the mean 72.4 and the standard deviation 5.9, but chance scored 46 in the class with the mean 52 and the standard deviation 7.5. who scored relatively better? (round the answers to 2 decimal places)
jaydens z - score is
and chances z - score is
. since jaydens z - score is select an answer chances z - score, 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 raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate Jayden's z - score

Given $x = 67$, $\mu=72.4$, and $\sigma = 5.9$. Then $z_{Jayden}=\frac{67 - 72.4}{5.9}=\frac{- 5.4}{5.9}\approx - 0.92$.

Step3: Calculate Chance's z - score

Given $x = 46$, $\mu = 52$, and $\sigma=7.5$. Then $z_{Chance}=\frac{46 - 52}{7.5}=\frac{-6}{7.5}=- 0.80$.

Answer:

Jayden's z - score is $-0.92$ and Chance's z - score is $-0.80$. Since Jayden's z - score is less than Chance's z - score, we conclude that Chance scored relatively better.