Ch. 4 REVIEW PROBLEMS 109 



6. Perform the operations required in problem 5 for all the birth weights of 

 female guinea pigs listed in Table 2.61. 



7. Perform the operations required in problem 5 for all the birth weights of 

 male guinea pigs listed in Table 2.61. 



8. Perform the operations required in problem 5 for all the 4-day gains of 

 female guinea pigs listed in Table 2.62. 



9. Perform the operations required in problem 5 for all the 4-day gains of 

 male guinea pigs listed in Table 2.62. 



10. Perform the operations required in problem 2 for logarithms to the 

 natural base e rather than 10, and comment on the effect of this change on the 

 graph. 



REVIEW PROBLEMS 



1. If you are among 1000 persons, each of whom purchases a one-dollar lot- 

 tery ticket for a prize of $1000, what is the expected value of your ticket in 

 the mathematical sense? 



2. Determine the expected frequencies of sums of 3, 4, 5, and 6, respectively, 

 when three unbiased dice are thrown simultaneously 1000 times. 



Ans. 4.6, 13.9, 27.8, 46.3. 



3. If 25 pennies and 15 dimes are placed in individual envelopes, thoroughly 

 mixed, and presented to you for the selection of one envelope, what is the 

 probability that you will get a dime? What is your mathematical expectation 

 on such a draw? 



4. How many two-digit numbers can you make up by selecting any number 

 from 1 to 9, inclusive, for each digit? How many numbers could you form if 

 none is to contain the same digit twice? Ans. 81, 72. 



5. Suppose that a turtle is hatched at point A and then wanders over a uni- 

 form terrain in search of food. If he never wanders more than 1000 yards 

 radially from spot A, and if he moves over the area in such a way that he is 

 equally likely to be on any preassigned areas of a specified size, what is the 

 probability that he will be within a circular area of 100 square yards whose 

 center is 300 yards from, and northeast of, the spot A? 



6. Table A (below) and Figure A present the distributions of the various sizes 

 of farms in Ness County, Kansas. If a stratoliner were to drop a package by 

 parachute so that it will be sure to land on Ness County, but the pilot cannot 

 tell where, what is the probability that it will fall on a farm of more than 

 1000 acres if 10 per cent of the county is not in farm land and that 10 per cent 

 is uniformly distributed over the county? Ans, .30. 



7. If 100 farmers are to be selected from Ness County without knowledge of 

 the areas of their farms, and if one supposes one farmer per farm, what is the 

 mathematically expected number of representatives from farms covering less 

 than 500 acres? What fraction of the county's farm acreage do they represent? 



8. Determine graphically the lower limit of the sixtieth percentile and of 

 the third decile for the data of Table A. Ans. About 520 acres; 260 acres. 



9. Table B presents a summary of the years of schooling had by all legal 

 residents of Kansas who were 25 years of age or older on April 1, 1940. Con- 

 struct what appears to you to be a good graphic presentation of these data. 



