[EX02-143] Each year, NCAA college football fans like to learn about the up-and-coming freshman class of players. Following are the heights (in inches) of the nation’s top 100 high school football players for 2005, as rated by recruiting analyst Tom Lemming of ESPN.com:

75 70 71 75 76 76 70 72 70 75 75 68 73 75 74 74 73 75 77 75 72 77 73 73 72 71 78 79 80 74 73 79 78 77 73 74 74 72 73 75 68 72 72 73 72 70 76 73 74 76 74 76 74 78 75 77 77 78 74 73 76 70 76 77 77 70 73 75 76 73 75 76 78 75 71 78 75 76 77 78 75 76 74 74 79 73 74 76 71 74 71 76 76 74 76 76 76 72 76 73 Source: ESPN.com

a. Construct a histogram and one other graph of your choice that displays the distribution of heights.

b. Calculate the mean and standard deviation.

c. Sort the data into a ranked list.

d. Determine the values of ¯ x  s, ¯ x  2s, and ¯ x 

3s, and determine the percentage of data within 1, 2, and 3 standard deviations of the mean.

e. Do the percentages found in part d agree with the empirical rule? What does this imply? Explain.

f. Do the percentages found in part d agree with Chebyshev’s theorem? What does that mean?

g. Do the graphs show a distribution that agrees with your answers in part e? Explain.