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 7.07 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. What range of times covers the middle 68% of this distribution? From to minutes Round to 2 places. What percent of these runners run the mile between 5.67 and 7.77 minutes? % Round to 2 places. What percentage of the these running times are faster than 9.17 minutes? % Round to 2 places.

Answer 1

Ans:

Empirical rule:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations.
• 99.7% fall within three standard deviations.

a)

68% of the data falls within one standard deviation of mean.

lower limit=7.07-0.7=6.37

upper limit=7.07+0.7=7.77

b)

5.67 falls 2 standard deviations below and 7.77 falls one standard deviation above the mean.

percent of these runners run the mile between 5.67 and 7.77 minutes=(0.95/2)+(0.68/2)=0.815 or 81.5%

c)

percentage of the these running times are faster than 9.17 minutes=(1-0.997)/2=0.0015 or 0.15%