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: Calculate z - score for Test A

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the individual score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For Test A: \(x = 62\), \(\mu=80\), \(\sigma = 6\)
\(z_A=\frac{62 - 80}{6}=\frac{-18}{6}=-3\)

Step2: Calculate z - score for Test B

For Test B: \(x = 70\), \(\mu = 90\), \(\sigma=10\)
\(z_B=\frac{70 - 90}{10}=\frac{-20}{10}=-2\)

Step3: Compare z - scores

Since \(-2>-3\), a higher z - score (closer to 0) means a better performance relative to the class.

Answer:

D. Test A: \(-3\); Test B: \(-2\); Test A