Question

Jane and Leah began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Jane took a test in English and earned a 70.5, and Leah took a test in Math and earned a 68.1. Use the fact that all the students' test grades in the English class had a mean of 75.9 and a standard deviation of 11.8, and all the students' test grades in Math had a mean of 66.5 and a standard deviation of 9.8 to answer the following questions.

a) Calculate the z-score for Jane's test grade.
z= [Round your answer to two decimal places.]


b) Calculate the z-score for Leah's test grade.
z= [Round your answer to two decimal places.]


c) Which person did relatively better?

• Jane
• Leah
• They did equally well.

Answer 1

Question (a)

Jane took a test in English and earned a 70.5

the students' test grades in the English class had a mean of 75.9 and a standard deviation of 11.8

So = 75.9

= 11.8

X = 70.5

z-score = (X - ) /

= (70.5 - 75.9) / 11.8

= -5.4 / 11.8

= -0.45763

= -0.46 rounded to 2 decimal places

So z-score for Jane's test grade = -0.46

Question (b)

Leah took a test in Maths and earned a 68.1

the students' test grades in the Maths class had a mean of 66.5 and a standard deviation of 9.8

So = 66.5

= 9.8

X = 68.1

z-score = (X - ) /

= (68.1 - 66.5) / 9.8

= 1.6 / 9.8

= 0.163265

= 0.16 rounded to 2 decimal places

So z-score for Leah's test grade = 0.16

Question (c)

Since the z-score of Leah's is more than that of Jane's, Leah did relatively better

So Answer is Option B