[EX02-144] Each year, NCAA college football fans like to learn about the size of the players in the current year’s recruit class. Following are the weights (in pounds) of the nation’s top 100 high school football players for 2005, as rated by recruiting analyst Tom Lemming of ESPN.com.

Just because these data are taken from the same 100 football players as in Exercise 2.143 does not mean the distributions will be the same. In fact, they are quite different, as you are about to see.

207 220 218 215 215

••• Remainder of data on Student’s Suite CD-ROM Source: ESPN.com

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

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.