Ch. 3 



REVIEW PROBLEMS 



73 



bilities of living to those successive ages are .74, .72, and .70, what should this 

 person pay for an annuity of this sort if the company is allowed 15 per cent for 

 overhead? Ans. 



REVIEW PROBLEMS 



1. What is the difference between a population of numerical measurements 

 and a sample of such measurements? 



2. What was Political Arithmetic? With what sorts of problems were the 

 political arithmeticians mainly concerned? 



3. Who was Student and how was his work connected with present types of 

 statistical problems? 



4. Expand (1/3 + 2/3) 4 into a series and state specifically what probability 

 is given by each term if p = 2/3 is the probability that a certain loaded penny 

 will turn up heads on any particular future throw. Describe the mathematical 

 procedure needed here to define the single events. 



5. What is a frequency distribution? A relative cumulative frequency dis- 

 tribution ? 



6. Suppose that a college freshman has earned the following percentile ratings 

 on the indicated tests: (a) general intelligence, 90; (b) achievement in social 

 sciences, 65; (c) achievement in physical sciences, 92; (d) achievement in 

 mathematics, 95. What can you say about the student's probable future success 

 in courses in chemistry, physics, mathematics, history, and sociology if it is 

 assumed that the tests are trustworthy and if no serious personal problems 

 interfere? 



7. Given that for a set of numerical measurements A r 1 , A%, . . . , -V50. SX = 95 

 and 2(x 2 ) = 2.06, calculate the coefficient of variation. 



8. Calculate the geometric, arithmetic, and harmonic means of 1/2, 2, and S 

 and discuss the choice of the best average for these numbers. Ans. 2, 3.5, 8/7. 



9. Suppose that the following probabilities regarding football games have been 

 determined reliably: A to beat B, p 1 = 2/3; C to beat D, p 2 = 1/2; and E to 

 beat F, p 3 = 5/6. What are the odds that A, D, and E all win? 



10. Given that the graph below is the r.c.j. curve for a certain group of scores, 

 determine from it the median, the upper limit of the third quartile, and the 

 upper limit of the sixth decile. Also interpret these results statistically, with 

 some indication of the uses to which such information can be put. 



Ans. 31.5, 41.0, 35.0. 



5 10 15 20 25 30 35 40 45 50 55 60 65 



Score 



