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Unformatted text preview: np is the same as E S n and np (1-p ) is the same as Var S n . So the ratio is also equal to ( S n-E S n ) / Var S n , and this ratio has mean 0 and variance 1, the same as a standard N (0 , 1). Note that here p stays xed as n , unlike the case of the Poisson approximation. Example. Suppose a fair coin is tossed 100 times. What is the probability there will be more than 60 heads? Answer. np = 50 and p np (1-p ) = 5. We have P ( S n 60) = P (( S n-50) / 5 2) P ( Z 2) . 0228 . Example. Suppose a die is rolled 180 times. What is the probability a 3 will be showing more than 50 times? 17...
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- Spring '09