Question

How fast can male college students run a mile? There’s lots of variation, of course. During World War II, physical training was required for male students in many colleges, as preparation for military service. That provided an opportunity to collect data on physical performance on a large scale. A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.09 minutes and standard deviation 0.7 minute.

It's good practice to draw a Normal curve on which this mean and standard deviation are correctly located. To do this, draw an unlabeled Normal curve, locate the points where the curvature changes (this is 1 standard deviation from the mean), then add number labels on the horizontal axis.

Use the Empirical Rule to answer the following questions.

A) range of times covers the middle 68% of this distribution?

From _____ to ______ minutes Round to 2 places.

B) What percent of these runners run the mile between 4.99 and 7.79 minutes?
_____________% Round to 2 places.

C) What percentage of the these running times are faster than 8.49 minutes?
_______________ % Round to 2 places.

Answer 1

According to a study of 12,000 able-bodied male students at the University of Illinois, their times for the mile run were approximately Normal with mean **7.11 minutes** and standard deviation **0.74 minute**¹.

Using the Empirical Rule:

A) The range of times that covers the middle 68% of this distribution is from **6.37 to 7.85 minutes** ¹.

B) The percentage of these runners who run the mile between 4.99 and 7.79 minutes is **99.73%** ¹.

C) The percentage of these running times that are faster than 8.49 minutes is **6.68%** ¹.

I hope this helps!