Extra exercise 7
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Accuracy of the 68-95-99.7 rule.

(a) Placing the flags of the applet one standard deviation on either
side of the mean gives an area of 1-2*0.1587 = 0.6826
- slightly more than the 0.68 of the rule.


(b) Two standard deviations: area = 1-2*0.0228 = 0.9544,
    Three standard deviations: area = 1-2*0.0013 = 0.9974.


(c) Human pregnancies follow N(266,16).

(i) 99.7% of human pregnancies lie within 266 +- 3*16 = (218,314).
    
(ii) Pregnancies longer than 282 days (mean + 1 standard deviation) 
occur with frequency (100%-68%)/2 = 16%. This is half of the area under
the curve (probability) outside the mean +- 1 standard deviation
 - which is (100%-68%)=32%.