Unformatted text preview: ≈ P ( Z ≥ 2) ≈ . 0228 . An example. Suppose a die is rolled 180 times. What is the probability a 3 will be showing more than 50 times? Answer. Here p = 1 6 , so np = 30 and p np (1p ) = 5. Then P ( S n > 50) ≈ P ( Z > 4) , which is very small. An example. Suppose a drug is supposed to be 75% eﬀective. It is tested on 100 people. What is the probability more than 70 people will be helped? Answer. Here S n is the number of successes, n = 100, and p = . 75. We have P ( S n ≥ 70) = P (( S n75) / p 300 / 16 ≥ 1 . 154) ≈ P ( Z ≥ 1 . 154) ≈ . 87 . (The last ﬁgure came from a table.) 41...
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 Spring '10
 ansan
 Approximation, Binomial, Central Limit Theorem, Normal Distribution, Probability theory, Binomial distribution, Sn

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