94 



BINOMIAL AND NORMAL DISTRIBUTIONS 



Ch. 4 



TABLE 4.23 



Ordered Batting Averages for Indicated Years Before and After 

 Conversion to Standard Normal Units 



(Includes higher ranking batters who were in at least 75 games during the 



season.) 



standard normal units are employed. In these units, his average 

 is a decided stand-out, being 0.26 unit ahead of the runner-up. 

 (c) In general, there is reason to believe that the batters in the year 

 1940 were not up to the standards of the other years shown in Table 

 4.23, especially those of 1920 and 1930. 



PROBLEMS 



1. Graph the normal frequency distribution with /i = 4 and a = 2 directly 

 from equation 4.21. 



2. Graph the normal distribution of problem 1, using formula 4.23. 



3. Graph the normal curve which approximates the binomial frequency dis- 

 tribution with n = 8 and p = 1/2. Do likewise for the binomial with n = 8 and 

 p = 1/4, and note the decrease in the goodness of the approximation. 



