Question

gregorio took two tests. find his z - score for each test. (remember: the number of standard deviations between a score and the mean score is indicated by a z - score.) on which did he score better compared with others in his class? test a test b gregorios score 62 70 mean score 80 90 standard deviation 6 10 a. test a: 3; test b: 2; test a c. test a: - 2; test b: - 3; test a b. test a: - 3; test b: - 2; test b d. test a: - 3; test b: - 2; test a please select the best answer from the choices provided

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the individual score, $\mu$ is the mean score, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for Test A

For Test A, $x = 62$, $\mu=80$, $\sigma = 6$. Then $z_A=\frac{62 - 80}{6}=\frac{-18}{6}=-3$.

Step3: Calculate z - score for Test B

For Test B, $x = 70$, $\mu = 90$, $\sigma=10$. Then $z_B=\frac{70 - 90}{10}=\frac{-20}{10}=-2$.

Step4: Compare z - scores

The higher the z - score, the better the performance relative to the class. Since $- 2>-3$, Gregorio scored better on Test B compared to his class.

Answer:

b. Test A: -3; Test B: -2; Test B