Question

The grades on the last history exam had a mean of 80%. Assume the population of grades on history exams is known to be distributed normally, with a standard deviation of 5%. Approximately what percent of students earn a score between 70% and 80%?

Answer 1

To calculate for the percent of students who earned scores of 70% and 80%, we compute for the z-scores first and translate the answer to percentiles.

z-scores calculation:

(70%) z-score = (70 – 80)/5 = -2

This translates to percentile of 2.28%

(80%) z-score = (80 – 80)/5 = 0

This translates to percentile of 50%.

Subtracting the percentiles will give us the final answer of 47.72%.