Question

8. Suppose you earned a score of 17 on a quiz. For which of the following conditions would your score indicate the best performance in relation to the rest of the class? Below are possible overall means and standard deviations for everyone who took the test. Which choice gives you the highest grade relative to everyone else?

A. mean 15, standard deviation 2.4

B. mean 15, standard deviation 2.1

C. mean 14, standard deviation 3.4

D. mean 16, standard deviation 1.4

Answer 1

We need to calculate the Z score for the each options. Higher Z score means the best performance.

For Random variable X with mean and standard deviation the z score is

Here , X = 17

A.   = 0.83

B. = 0.95

C. = 0.88

D. = 0.71

Clearly the Z score is maximum for Option B.

So mean 15 and standard deviation 2.1 gives you the highest grade relative to everyone else.