The scores on an exam are normally distributed with a mean of 70 and a standard deviation of 8. Approximately what percentage of scores fall between 62 and 78?

Step 1: Compare the endpoints with the mean.

The mean is 70 and the standard deviation is 8.

The lower endpoint is:
62 = 70 - 8

So 62 is one standard deviation below the mean.

The upper endpoint is:
78 = 70 + 8

So 78 is one standard deviation above the mean.

Step 2: Recognize the interval.

The interval from 62 to 78 represents values within one standard deviation of the mean.

Step 3: Apply the Empirical Rule.

For a normal distribution, approximately 68% of observations fall within one standard deviation of the mean.

Therefore, approximately 68% of the exam scores fall between 62 and 78.