74 



ELEMENTARY PROBABILITY 



Ch. 3 



11. What proportion of the scores summarized in problem 10 lay between 40 

 and 60 inclusive? What proportion exceeded 60? 



12. What is the probability that on 15 flips of an unbiased penny one will get 

 either 7 or 8 heads? Will get neither 7 or 8 heads? Ans. .39, .61. 



13. Suppose that for a certain strain of chickens the probability that a late- 

 feathering chick will be hatched from any egg selected at random is 1/16. What 

 is the expected number of such late-feathering chicks among 800 newly hatched 

 chicks? 



14. If a pair of true dice is rolled 60 times, what is the mathematically ex- 

 pected number of sevens? Of either sevens or elevens? Of sums greater than 9? 



Ans. 10, 13y 3 , 10. 



15. Assume that the semester grades in a large chemistry class have the 

 ogive graphed below. If the letter grades are to be distributed as follows: 

 7 per cent A, 20 per cent B, 46 per cent C, 20 per cent D, and 7 per cent F, 

 what are the grade ranges covered by each letter grade? 



1.00 



9J .80 



60 70 



Grade 



16. What is the median numerical grade for the data of problem 15 above? 

 What are the upper limits of the quartiles? Ans. 69; 59.5, 69, 77, 100. 



17. Suppose that 6 unbiased pennies are to be tossed simultaneously. What 

 is the probability that no more than 2 will show heads? That at least 2 will 

 turn up heads? 



18. Assume that the true odds on each of 3 horses to win a particular race 

 are determined to be as follows: horse A, 3:2; horse B, 1:3; and horse C, 1:9. 

 What is each horse's probability of winning? What is the probability that 

 some one of these 3 horses will win? Ans. .60, .25, .10; .95. 



19. Given that for three separate statistical populations of data: ^ — 25, 

 a 1 = 4; ix. 2 = 50, ov, = 5; and ^3 = 100, <r 8 = 13. Which group of data would 

 you consider as relatively the more variable? Give specific statistical evi- 

 dence to back your answer. 



20. Compute the mean deviation and the standard deviation for the fol- 

 lowing data: 13, 9, 10, 17, 15, 20, 11, 5, 2, 10, 14, 13, 19, 21, 16, 8, 14, 6, 3, 29, 16, 

 17, 15, 15, 18, and 2. Which measure of variation do you think best describes 

 the dispersion of these data about their arithmetic mean? Give reasons. You 

 are given that 2Z = 338, 2LY2 = 5406. Ans. 4.92, 6.24. 



