Question

Suppose that the distribution of exam scores in a class of 200 student is a normal distribution. Also suppose that the distribution's mean is 75 points, and its standard deviation is 10.

Use the 68-95-99.7 rule to determine what percent of the scores do we expect to fall above 65? %

Answer 1

Using the 68-95-99.7 rule and the properties of a normal distribution with a mean of 75 and standard deviation of 10, we conclude that 84% of exam scores are expected to fall above 65 points.

Step-by-step explanation:

To determine what percent of the exam scores we expect to fall above 65 points in a class of 200 students with a normal distribution, a mean of 75 points, and a standard deviation of 10 points, we can use the 68-95-99.7 rule (also known as the empirical rule). The rule tells us that:

• 68% of the data falls within one standard deviation of the mean (75 ± 10), so between 65 and 85.
• 95% falls within two standard deviations (75 ± 20), so between 55 and 95.
• 99.7% falls within three standard deviations (75 ± 30), so between 45 and 105.

According to this rule, 68% of the scores are between 65 and 85. Since the distribution is symmetrical, half of the 68%, which is 34%, falls below 75 and the other half above 75. However, since 65 is only one standard deviation below the mean, we also have the upper half (50%) of the distribution above 65. Therefore, if we add the 34% and 50%, we get that 84% of the scores fall above 65 points.