Question

Todd and Garrett began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Todd took a test in Math and earned a 74.6, and Garrett took a test in English and earned a 68.8. Use the fact that all the students' test grades in the Math class had a mean of 70.6 and a standard deviation of 11.9, and all the students' test grades in English had a mean of 63.7 and a standard deviation of 8.6 to answer the following questions.

Required:
a. Calculate the z-score for Todd's test grade.
b. Calculate the z-score for lan's test grade.
c. Which person did relatively better?

Answer 1

Part A

For Todd's class, we have this given info:

• mu = 70.6 = population mean of math scores
• sigma = 11.9 = population standard deviation of math scores

Compute the z score for x = 74.6

z = (x-mu)/sigma

z = (74.6 - 70.6)/(11.9)

z = 0.34 approximately

Side note: Convention usually has z scores rounded to two decimal places. If your teacher instructs otherwise, then go with those instructions of course.

Answer: 0.34

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Part B

For Garret's English class, we have:

• mu = 63.7
• sigma = 8.6

Compute the z score for x = 68.8

z = (x-mu)/sigma

z = (68.8 - 63.7)/(8.6)

z = 0.59 approximately

Answer: 0.59

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Part C

Garret has the higher z score, which means that Garret did relatively better to his classmates compared to Todd's performance (in relation to his classmates). The z score is the distance, in units of standard deviation, the score is from the mean. Positive z values are above the mean, while negative z values are below the mean.

Answer: Garret did relatively better