Question

Professor Hopkins is grading the final exam. She notices that the

mean test score is 71, and the standard deviation is 6. The test
scores were normally distributed.
If there were 300 students in the data sample, how many would
have a test score between 71 and 83?*
*Round your answer to the nearest whole value.
students

Answer 1

143

Explanation:

The interval of interest extends from the mean score (71) to 2 standard deviations above the mean (71+2(6) = 83). The area under the normal distribution curve in this interval can be found using a suitable table, probability app, spreadsheet, or web site. It can also be found using the "empirical rule", which tells you that the 95% of the area is within 2 standard deviations of the mean.

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Since the curve is symmetrical, and we're only interested in the area above the mean, the empirical rule tells us that 95%/2 = 47.5% of the sample will be in the range of interest.

0.475 × 300 = 142.5 ≈ 143

143 students will have a score between 71 and 83.

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The attachment shows a calculator output for the same calculation. You will notice it is slightly different from the "empirical rule," which is only an approximation. Either way, we find 143 students have scores in the range.