[EX02-207] Each year, stock car drivers compete for NASCAR. Points are earned on the basis of finishes in sanctioned races scheduled on the circuit. At the end of the 2004 season, the standings posted at NASCAR.com; the top 32 drivers are shown in the following table.

Driver Points Driver Points Kurt Busch 6506 Jimmie Johnson 6498

••• Remainder of data on Student’s Suite CD-ROM Source: NASCAR

a. Draw a dotplot.

b. Calculate the mean and standard deviation of the points accumulated by the NASCAR drivers.

c. Construct a 5-number summary table and draw a box-and-whiskers display.

d. According to Chebyshev’s theorem, at least 75% of the points will fall between what two amounts? Is this the case?

e. According to the empirical rule, approximately 68% of the points will fall between what two amounts? Is this the case?

f. Compare your answers to parts d and e to the results predicted by the empirical rule. Does your comparison suggest that the distribution of NASCAR points approximates the normal distribution? Explain.

g. (Optional.) The 2004 season had a total of 88 drivers earning points. The complete list of 88 drivers is included in the data file for this exercise.

Using all 88 pieces of data, answer the questions in parts a through

e. [DS02-207]