Question

Suppose the z-score of your grade on this Statistics exam turns out to be z=0.87. Which of the following is the best interpretation of this z

-score?

I answered 87% of the questions correctly.

a. My grade is the 87th percentile.
b. My grade is 0.87 points above the mean.
c.My grade is 0.87 standard deviations above the mean.

Answer 1

c.My grade is 0.87 standard deviations above the mean.

Explanation:

given that the z-score of your grade on this Statistics exam turns out to be z=0.87.

Z score is nothing but std normal variate

Any normal distribution can be converted into std normal by the transformation

Z =
`(x-\mu)/(\sigma)`

Thus when z=0.87 we mean

x = Mean +0.87 sigma

Or my grade is 0.87 std deviations above the mean

Hence option C is right.

c.My grade is 0.87 standard deviations above the mean.