110 



BINOMIAL AND NORMAL DISTRIBUTIONS 



Ch. 4 



10. If a roving reporter were to go all over Kansas, impartially asking persons 

 their opinions on a certain educational matter, what proportion of his inter- 

 views would you expect to be with persons who have had at least two years 

 of college education if he talked only to persons who were at least 25 on 

 April 1, 1940? What percentage would have no college education? 



Arts. 9 per cent, 88 per cent. 



11. If an insecticide is known to be 99 per cent lethal to a certain species of 

 insect, what is the probability that less than 5 will survive if 150 selected at 

 random are sprayed with this spray? 



12. Suppose that a particular variety of apple grown under specified condi- 

 tions produces yields (per tree) which are normally distributed with n = 8 

 bushels and a = 2.5 bushels. What is the probability that a randomly chosen 

 tree will be found to yield less than 5 bushels? That two such trees will each 

 be found to yield less than 5 bushels? Ans. .12, .014. 



13. Obtain records like those in Table B from the latest census, make an r.c.j. 

 graph for those data, and determine the median years of schooling. Compare 

 with the median for 1940 and draw any appropriate conclusions. Use college 

 years as 13, 14, 15, 16, and 17. 



14. Plot the r.c.j. distribution of Table A on normal-arithmetic paper and 

 comment on the apparent normality, or lack of it, for this distribution of farm 



1 201 401 601 



Figure A. 



801 1001 1201 1401 1601 1801 2001 

 Acres 



Two types of relative cumulative frequency distributions for the 

 sizes of farms in Ness County, Kansas, in 1940. 



