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12 Figure 2. There does not seem to be very much variation, but it is worth checking how much variation we would expect if the numbers were, in fact, randomly chosen. If they were, the numbers of occurrences of a particular number, say 17, would have a binomial distribution with n = 102,006 and p = 1/45. Such a distribution has mean np and standard deviation npq where q = 1–p. This gives mean 2267 and standard deviation 47. It would be unusual to see differences of more than three standard deviations, or 141, from the mean. It is hard to tell the actual differences from the graph, so we looked at the actual data. We found that, for all but two numbers, the results were within two standard deviations of the mean. For the other 2 numbers the results were within 3 standard deviations of the mean. Thus the picks chosen by the computer do not appear to be inconsistent with the random model. A ChiSquare test would give a way to proceed with a formal test of this hypothesis. We look next at the picks chosen by the players. Recall that we have the same number 17,001 of picks so we again have 102,006 individual numbers.PDF Image | USING LOTTERIES IN TEACHING A CHANCE COURSE
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