Question

Cheick and Miranda began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Cheick took a test in English and earned a 79.1, and Miranda took a test in Math and earned a 72. Use the fact that all the students' test grades in the English class had a mean of 72.9 and a standard deviation of 12.1, and all the students' test grades in Math had a mean of 60.8 and a standard deviation of 10.3 to answer the following questions.

a) Calculate the z-score for Cheick's test grade.



b) Calculate the z-score for Miranda's test grade.



c) Which person did relatively better?
Cheick
Miranda
They did equally well.

Answer 1

See below for answers and explanations

Explanation:

Z-score for Cheick

`\displaystyle Z=\frac{\bar{x}-\mu}{\sigma}=(79.1-72.9)/(12.1)=(6.2)/(12.1)\approx0.51`

Z-score for Miranda

`\displaystyle Z=\frac{\bar{x}-\mu}{\sigma}=(72-60.8)/(10.3)=(11.2)/(10.3)\approx1.09`

Therefore, since Miranda's z-score is greater than Cheick's, Miranda did relatively better.