Question

Catherine and Amy began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Catherine took a test in Math and earned a 72.1, and Amy took a test in English and earned a 64.1. Use the fact that all the students' test grades in the Math class had a mean of 72.6 and a standard deviation of 10.5, and all the students' test grades in English had a mean of 60.4 and a standard deviation of 9.1 to answer the following questions.a) Calculate the z-score for Catherine's test grade.z= b) Calculate the z-score for Amy's test grade.z= c) Which person did relatively better?CatherineAmyThey did equally well.

Answer 1

A) z = -0.05

B) z = 0.41

C) Amy

Explanation:

Remember that the formula we use to calculate a z-score is:

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \\ \mu=\text{ mean} \\ \sigma\text{ = standard deviation} \end{gathered}`

Let's calculate the z-score for Catherine's test grade:

`\begin{gathered} Z_C=(72.1-72.6)/(10.5) \\ \\ \Rightarrow Z_C=-0.05 \end{gathered}`

Now, let's calculate the z-score for Amy's test grade:

`\begin{gathered} Z_A=(64.1-60.4)/(9.1) \\ \\ \Rightarrow Z_A=0.41 \end{gathered}`

Since the z-score for Amy's test grade is greater than Catherine's, we can conclude that Amy perfomed better.