So THEORY OF STATISTICS. 
7. Taking the mean stature for the British Isles as 67°46 in. (the dis- 
tribution of fig. 49), the mean for Cambridge students as 68:85 in., and the 
common standard-deviation as 2:56 in., what percentage of Cambridge students 
exceed the British mean in stature, assuming the distribution normal % 
8. As stated in Chap. X1l[., Example ii., certain crosses of Pisum sativum 
based on 7125 seeds gave 25°32 per cent. of green seeds instead of the theoretical 
proportion 25 per cent., the standard error being 0°51 per cent. In what per- 
centage of experiments based on the same number of seeds might an equal or 
greater percentage be expected to occur owing to fluctuations of sampling 
alone? 
9. In what proportion of similar experiments based on (1) 100 seeds, (2) 
1000 seeds, might (a) 30 per cent. or more, (5) 35 per cent. or more, of green 
seeds, be expected to occur, if ever ? 
10. In similar experiments, what number of seeds must be obtained to 
make the ‘¢ probable error ” of the proportion 1 per cent. ? 
11. If skulls are classified as dolichocephalic when the length-breadth 
index is under 75, mesocephalic when the same index lies between 75 and 80, 
and brachycephalic when the index is over 80, find approximately (assuming 
that the distribution is normal) the mean and standard-deviation of a series 
in which 58 per cent. are stated to be dolichocephalic, 38 per cent. meso- 
cephalic, and 4 per cent. brachycephalic, 
216