Standard deviation

Question

The scores on a psychology exam were normally distributed with a mean of 68 and a standard deviation of 8. What is the standard score for an exam score of 83?

Answer 1

83-68= 15

15/8 = 1.875 = z score

use z tables, a z calculator on line or a hand calculator with a statistics function.

1.875 is almost 2 deviations from the mean, by the empirical rule 95 % of the scores are between 2 standard deviations from the mean, with half of 5% or 2.5% above 83. 83 is about the 97.5 th percentile, but slightly less because 1.875 is slightly less than 2.

by z calculators on line, 1.875 means about 96.96% or 97% scores are less than 83

Grading on a normal curve would mean a 97 if you scored an 83