Sec. 4.3 FRACTION OF X'S WITHIN GIVEN LIMITS 95 



4. Graph as in problem 3, with n = 12 instead of 8, and comment on the 

 effect of increasing the size of n. 



5. Graph the frequency curve for a normal population with fi — 10 and 

 ff = 2, and estimate roughly from the graph the proportion of all the measure- 

 ments in this population which are greater than or equal to 12. 



6. Make a frequency distribution table for the birth weights of male guinea 

 pigs as recorded in Table 2.61, compute the fi and a, and then graph the normal 

 curve with the same /j. and a. How does the graph compare with the frequency 

 distribution curve made directly from your distribution table? 



7. Perform the operations of problem 6, using the records for the female 

 guinea pigs in Table 2.61. 



8. Perform the operations of problem 6, using the 4-day gains of male guinea 

 pigs as listed in Table 2.62. 



9. Perform the operations of problem 6, using the 4-day gains of female 

 guinea pigs as given in Table 2.62. 



10. Graph the binomial frequency distribution for n = 16 and p = 1/2 and 

 then plot the corresponding normal distribution on the same axes, adjusting 

 the height to fit the binomial. Also construct for each value of r a rectangle 

 of base r — 1/2 to r + 1/2 and height = C 16 r -p'q w — r . Then indicate on your 

 graph the area under the normal curve which is approximately equal to 

 P(8^r^ 11), the probability that r will have a value from 8 to 11, inclusive. 



11. Perform the operations of problem 10, with p = 3/5. 



12. Choose any available source and compare the batting averages in the 

 National League for 1940 and 1950, using the leading 25 players in each year 

 and converting the batting averages to standard normal units. 



4.3 DETERMINATION OF THE PROPORTION OF A NOR- 

 MAL POPULATION OF MEASUREMENTS INCLUDED 

 BETWEEN ANY SPECIFIED LIMITS 



In Chapter 2 the student was given the opportunity to learn how 

 to construct an r.c.f. distribution, how to graph it, and how to deter- 

 mine from this graph the limits on A" which would include any 

 specified proportion of the data so summarized. Furthermore, the 

 inverse process also was discussed, namely, the determination of the 

 proportion of the data which lies within specified limits. It is de- 

 sirable to be able to obtain the same sort of information for nor- 

 mally distributed groups of measurements. The basis for such a 

 procedure was given in the preceding section. 



There is, however, one major difference between the process taught 

 in Chapter 2 and that which is necessary to handle the standard 

 normal frequency distribution. In the latter situation there is no 

 distribution table with class intervals and cumulative frequencies 

 determined by means of certain arithmetic procedures. Instead the 

 r.c.f. distribution must be derived from the formula for the normal 



