Question

Samantha took an exam in her statistics class and received 90 out of 100. Samantha thought that was a good score, but she wanted to know how high her score was in relation to the rest of the class. Her professor said her z-score was 1.29. How should Samantha interpret her z-score

Answer 1

Samantha's grade was 1.29 standard deviations above the class mean, that is, she scored better than 0.9015 = 90.15% of the class.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

She scored better a proportion of the class given by the p-value of z = 1.29

z = 1.29 has a p-value of 0.9015.

Samantha's grade was 1.29 standard deviations above the class mean, that is, she scored better than 0.9015 = 90.15% of the class.