ANSWERS, ETC., TO EXERCISES GIVEN. 
CHAPTER XV. 
(1) © 1 7 792 
12 8 495 
66 9 220 
220 10 66 
495 11:12 
. 792 12 1 
GU 924 —_ 
Total, 4096 
(2) 0 4594 5 1164 
1 1102+6 6.872 
r 1212-8 7 47 
¢ 8086 8 6 
4 3639 - - 
Total, 4096-2 
3) 0 192 
1 288 
2 144 
3 24 
Total, 648 
2. The frequency of r successes is greater than that of r—1 so long as 
r<np+p: if np is an integer, r =np gives the greatest term and also the mean. 
3. This follows at once from a consideration of the Galton-Pearson apparatus. 
Binomial Normal curve, 
1 17 
10 105 
45 427 
120 116-1 
210 211'5 
252 2584 
210 2115 
ete. ete. 
5. The data are //=68'855, 0 =256, y,=1558. 
6. (1) United Kingdom—direct 1°75, from standard-deviation 1°73. 
(2) Cambridge students—direct 168, from standard-deviation 1°73. 
7. 70°6 per cent. 8. 27 per cent. 
9. (1) In @ 12°4 per cent., b 10 per cent. of the trials, assuming normality, 
but the assumption is hardly quite valid. (2) a about 13 times in 100,000 
trials ; b practically impossible, being a deviation of over 7 times the standard 
error. 
10. 853. 11. Mean 74°3, standard-deviation 3°23, 
CHAPTER XVI. 
3. From equations (10) and (11) replace oy and oy by =; and =, in equation 
(9). Regarding this as an equation for , note that 7? is a maximum when 
tan 2 0 is infinite, or §=45°, 
405 
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