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 (or 0.6827, if
calculated directly) - slightly more than the 0.68 of the rule.


(b) Two standard deviations: area = 1-2*0.0228 = 0.9544 (0.9545)
    Three standard deviations: area = 1-2*0.0013 = 0.9974 (0.9973).


(c) Human pregnancies follow N(266,16). You may either change the mean
and standard deviation of the applet accordingly and base your answers
on its values, or apply the 68-95-99.7 rule directly (without using the
applet).

(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 probability (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%.