5 The following table gives the number of homes runs hit by the American League

home-run champions for the years 1949 to 1987, given in chronological order

beginning with 1949 and proceeding left to right across the rows. (Source:

Time Almanac 2004, page 1010.)

43 37 33 32 43 32 37 52 42 42 42 40 61

48 45 49 32 49 44 44 49 44 22 37 32 32

36 32 39 46 45 41 22 39 39 43 40 40 49

a. Find the meanand standard deviationof number of home runs hit by the

American League home-run champions during the years given in the table.

Column1

Mean 40.35897436

Standard Error 1.237344671

Median 41

Mode 32

Standard Deviation 7.727214993

Sample Variance 59.70985155

Kurtosis 0.969910322

Skewness -0.149774862

Range 39

Minimum 22

Maximum 61

Sum 1574

Count 39

The mean for the number of home runs hit by the American League home-run champions is 40.358974

The standard deviation for the number of home runs hit by the American League home-run champions is 7.727215

b. Assuming that the dataare approximately normally distributed, use the

empirical rule to find an interval of values within which approximately 68

percent of the data falls. Count the number of data values that actually fall

within that interval. Is it close to 68 percent?

c. Use the empirical rule to find the interval of values within which approximately

95 percent of the data falls. Count the number of data values that actually

fall within that interval. Is it close to 95 percent?

d. Use the empirical rule to find the interval of values within which approximately

99.7 percent of the data falls. Count the number of data values that actually

fall within that interval. Is it close to 99.7 percent?

The solution provides step by step method for the calculation of mean, standard deviation and the application of empirical rule in normal distribution. Formula for the calculation and Interpretations of the results are also included.