Ch. 3 REFERENCES 75 



21. According to Figure 2.41, in which quartile would you place a score of 85? 

 In which decile would this score fall? 



22. If all students whose ACE scores (Table 2.01) fell among the lower 15 

 per cent, approximately, of all scores made were to be advised to consider 

 seriously dropping out of college, what would be the highest score whose re- 

 cipient would receive such advice? Ans. 67. 



23. From Figure 2.41 determine approximately the percentage of those scores 

 which were not more than one times the standard deviation either greater than 

 or less than the mean, /*. 



24. In the game of "craps" two unbiased dice are thrown successively by the 

 same person. He wins if: (a) he throws a sum of either 7 or 11 on his first 

 throw; or (b) he throws a 4, 5, 6, 8, 9, or 10 on the first throw and repeats his 

 number on a subsequent throw before he throws a 7. What is his probability 

 of winning within 2 throws? Ans. 97/324. 



25. In a certain gambling game you are paid 15 for 1 if you throw a 1 and a 2 

 (either order) on two unbiased dice. On 1800 games on each of which the 

 player pays one dollar, what is the expected percentage profit for the house 

 relative to the amount taken in? 



REFERENCES 



Arley, Niels, and K. Rander Buch, Introduction to the Theory of Probability 

 and Statistics, John Wiley and Sons, New York, 1950. 



Kenney, John F., Mathematics of Statistics, Part II, Second Edition, D. Van 

 Nostrand Company, New York, 1947. 



Levy, H., and L. Roth, Elements of Probability, Oxford University Press, Lon- 

 don, 1936. 



