By Bouchaud J.-P.
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Suppose that the machine delivers a quantity of soup which is Normally distributed with mean IL litres and standard deviation a litres. 004, find the probability that a randomly chosen can contains less than the nominal volume. It is required by law that no more than 1 % of cans contain less than the nominal volume. 457. [MEI] 13 A factory is lit by a large number of electric light bulbs whose lifetimes are modelled by a Normal distribution with mean 1000 hours and standard deviation 110 hours.
Find the probability that he makes the coffee (i) too strong (ii) too weak (iii) all right. 44 4 When a butcher takes an order for a Christmas turkey, he asks the customer what weight in kilograms the bird should be. He then sends his order to a turkey farmer who supplies birds of about the requested weight. 75 kg. 2 Mrs Jones orders a 10 kg turkey from the butcher. 5 kg of the weight she actually ordered. 5 A biologist finds a nesting colony of a previously unknown sea bird on a remote island.
It is clearly so unlikely that this was a result of random sampling that another explanation must be found. O What do you think went wrong with the exit poll? Remember this really did happen. Approximating the Poisson distribution You may use the Normal distribution as an approximation for the Poisson distribution, provided that its parameter (mean) /I is sufficiently large for the distribution to be reasonably symmetrical and not positively skewed. As a working rule /I should be at least 10. 16.
An introduction to statistical finance by Bouchaud J.-P.