Use the 68-95-99.7 rule to solve the problem.
-For women at Hartford College, times to run 400 meters are normally distributed with a mean of 82 seconds and a standard deviation of 5 seconds. What percentage of the times are more than 67
Seconds?
A)99.7%
B)0.15%
C)0.3%
D)99.85%

Question

Quizplus · Accepted Answer

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In this case, a time of 67 seconds is three standard deviations below the mean (82 - 3*5 = 67). Therefore, 99.7% of the times are within three standard deviations, which includes times more than 67 seconds. Since we're looking for times more than 67 seconds, we need to include almost all the data except for the very small percentage (0.3%) that falls below 67 seconds. Thus, 100% - 0.3% = 99.7% of the data is more than 67 seconds, but since the options don't include 99.7% exactly and considering the slight approximation in the empirical rule, the closest and correct option is 99.85%.

Use the 68-95-99.7 Rule to Solve the Problem