a teacher gave a unit test to both of her statistics classes. the mean test grade for class a was 77 points…

a teacher gave a unit test to both of her statistics classes. the mean test grade for class a was 77 points, with a standard deviation of 5 points, whereas the mean test grade for class b was 80, with a standard deviation of 7 points. kyle, in class a, received an 82 on the test, and caleb, in class b, received an 87. whose performance on the unit test was better relative to their class?\ncaleb did better because his z - score is higher than kyles.\nkyle did better because his z - score is higher than calebs.\ncaleb did better because his z - score is closer to the mean.\nthey both performed the same because their z - scores have the same value.

a teacher gave a unit test to both of her statistics classes. the mean test grade for class a was 77 points, with a standard deviation of 5 points, whereas the mean test grade for class b was 80, with a standard deviation of 7 points. kyle, in class a, received an 82 on the test, and caleb, in class b, received an 87. whose performance on the unit test was better relative to their class?\ncaleb did better because his z - score is higher than kyles.\nkyle did better because his z - score is higher than calebs.\ncaleb did better because his z - score is closer to the mean.\nthey both performed the same because their z - scores have the same value.

Answer

Explanation:

Step1: Calculate Kyle's z - score

The formula for the z - score is (z=\frac{x-\mu}{\sigma}), where (x) is the data point, (\mu) is the mean, and (\sigma) is the standard deviation. For Kyle: (x = 82), (\mu=77), (\sigma = 5) (z_{Kyle}=\frac{82 - 77}{5}=\frac{5}{5}=1)

Step2: Calculate Caleb's z - score

For Caleb: (x = 87), (\mu = 80), (\sigma=7) (z_{Caleb}=\frac{87-80}{7}=\frac{7}{7}=1)

Answer:

They both performed the same because their z - scores have the same value.