Sec. 4.2 THE NORMAL FREQUENCY DISTRIBUTION 85 



7. Flip 3 pennies 80 times, recording the number of heads after each toss of 

 the 3 pennies. Then compare the observed and the mathematically expected 

 numbers of occurrences in each of the four possible classes of events in terms 

 of number of heads. 



8. Perform the operations of problem 7, except to compare the observed 

 and the theoretical values of the arithmetic mean. 



9. Suppose that a large group of fruit flies consists of members who are 

 classified as either "normal" or "sooty." Among 10 of these flies selected at 

 random, 3 were found to be "sooty." How frequently would that result be 

 obtained if half the flies in the population are "sooty"? How frequently if 25 

 per cent are "sooty"? 



10. Suppose that under the conditions of problem 9, 100 flies are chosen at 

 random and 30 (same percentage as in problem 9) are "sooty." Answer the 

 same questions as in problem 9. 



Ans. 23 times in 1,000,000; 12 times in 1 billion. 



11. Construct the r.c.f. distributions for problem 3 and then determine the 

 median r in each distribution. 



12. Suppose that there are two political parties interested in a certain college 

 election, and that 60 per cent of the eligible voters are Progressives and 40 per 

 cent are Independents. If a random sample of 10 persons is taken, what is the 

 probability that a plurality of them will be Independents, even though they 

 constitute the minority party? Ans. .17. 



13. Referring to problem 12, how large must the sample be before the proba- 

 bility is less than 1/4 that there will be more Independents than Progressives 

 in the sample? 



14. Suppose that 6 persons out of 10 selected at random in a certain city 

 favor a particular flood-control policy. What is the probability of such a result 

 when only 45 per cent of those in that city actually favor that policy? Ans. .16 



15. For problem 9 determine the median number of "sooty" flies among 10. 

 What is the probability that the actual number observed will exceed the 

 median? 



4.2 THE NORMAL FREQUENCY DISTRIBUTION 



A frequency distribution for a population of numerical measure- 

 ments is intended to display in some manner the density with which 

 the measurements are distributed along the scale on which they are 

 measured. Such a frequency distribution indicates the region (along 

 the scale of measurement) in which the measurements tend to be 

 most numerous, and also shows the way in which they are dispersed 

 about that region of concentration. The reader should see that these 

 are the same two general matters of concern considered in Chapter 

 2. Averages were used to measure general level of performance (as 

 on ACE scores), and measures like the standard deviation, mean 

 deviation, range, and quartiles were employed in the description of 

 the dispersion of the data along the scale of measurement. This sort 



