Question

The mean for Mr. Foster’s Financial Algebra test was 70, and the standard deviation was 4.2. Ms. Helmer’s mean for her test was 35, and the standard deviation was 5.7. Two friends were arguing about which did better on the test. Becky got a 78 on Mr. Foster’s test, whereas Erin got a 45 on Ms. Helmer’s test. Help settle the argument by selecting the most correct answer below. *

A: Becky has a Z-score of 1.90 while Erin has a Z-score of 1.75. Becky scored more standard deviations above the mean, therefore she did better on the test.

B: Becky has a Z-score of 1.90 while Erin has a Z-score of 1.75. Erin is closer to the mean, therefore she did better on the test than Becky.

C: Becky scored a 78 while Erin got a 45, so she scored much better on the test.

D: Erin exceeded the mean on her test by 10, while Becky only exceeded the mean by 8, so Erin did better on the test.

Answer 1

Becky and Erin's performance on their respective tests is best compared using Z-scores. Becky's Z-score was 1.90 while Erin's was 1.75, indicating that Becky scored relatively better on her test, being further above the mean than Erin.

Step-by-step explanation:

To settle the argument regarding which student did better on their respective test comparing Becky's score on Mr. Foster's test with Erin's score on Ms. Helmer's test, we need to calculate their Z-scores.

The Z-score is a statistical measure that tells us how many standard deviations an individual's score is from the mean of the group. The formula for calculating a Z-score is Z = (X - μ) / σ, where X is the score, μ (mu) is the mean, and σ (sigma) is the standard deviation.

For Becky:
Z = (78 - 70) / 4.2
Z = 8 / 4.2
Z = 1.90

For Erin:
Z = (45 - 35) / 5.7
Z = 10 / 5.7
Z = 1.75

Comparing the Z-scores, Becky's score is higher, meaning she scored more standard deviations above the mean than Erin did. Therefore, option A is the most correct: Becky has a Z-score of 1.90 while Erin has a Z-score of 1.75. Becky scored more standard deviations above the mean, therefore she did better on the test.