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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%?

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BlueSky06

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%. 

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