Question

When Lauren runs the 400 meter dash, her finishing times are normally distributed with a mean of 73 seconds and a standard deviation of 0.5 seconds. Using the empirical rule, what percentage of races will her finishing time be between 72 and 74 seconds?

a. 68%
b. 95%
c. 99.7%
d. 50%

Answer 1

The empirical rule indicates that approximately 68% of Lauren's races will have a finishing time between 72 and 74 seconds, as these times fall within one standard deviation of the mean.

Step-by-step explanation:

When Lauren runs the 400 meter dash and her finishing times are normally distributed with a mean of 73 seconds and a standard deviation of 0.5 seconds, we can use the empirical rule to determine what percentage of races will have her finishing time between 72 and 74 seconds. The empirical rule (also known as the 68-95-99.7 rule) states that for a normally distributed dataset:

• About 68% of the data falls within one standard deviation of the mean.
• About 95% falls within two standard deviations.
• About 99.7% falls within three standard deviations.

In this case, 72 and 74 seconds are one standard deviation below and above the mean, respectively. Therefore, according to the empirical rule, approximately 68% of her races will have a finishing time between 72 and 74 seconds.