Unformatted text preview: np is the same as E S n and np (1p ) is the same as Var S n . So the ratio is also equal to ( S nE 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 ﬁxed 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 (1p ) = 5. We have P ( S n ≥ 60) = P (( S n50) / 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
 wen
 Normal Distribution, Standard Deviation, Variance, Probability theory, Binomial distribution, Sn

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