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Normal Approximation of the Binomial Distribution

Normal Approximation of the Binomial Distribution. N(0,1)  Bin. Example.

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Normal Approximation of the Binomial Distribution

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  1. Normal Approximation of the Binomial Distribution N(0,1)  Bin

  2. Example • It is estimated that 15% of the Canadian population is undecided as to which political party to vote for in the next election. If a poll is conducted and 1007 citizens respond to the questionnaire, what is the probability that 100 or more of them are undecided?

  3. Binomial Distribution • X: the # of undecided citizens • n = 1007 Bernoulli trials • p = 0.15 • Find P( X >= 100)

  4. Binomial Distribution • X: the # of undecided citizens • n = 1007 Bernoulli trials • p = 0.15 • Find P( X >= 100)

  5. Solution • P( X >= 100) = P(100) + P(101) + P(102) + … + P(1007) • Whew!

  6. Time out… • Normal Approximation to the Binomial Distribution.xls • As p = 0.1 … to 0.9, …

  7. Approx. Binomial with N(,2) • Check np and nq • np = (1007)(0.15) = 151.05 • nq = (1007)(0.85) = 855.95 • If np > 5 and nq >5, then can approximate with X~N(np, npq)

  8. …back to the original problem •  = np = 151.05, • 2 = npq = (1007)(0.15)(0.85) = 128.39 • Approximate using X~N(151.05, 128.39)

  9. Solution

  10. Solution • Therefore, the probability that more than 100 out of 1007 people are undecided is nearly certain (99.99%).

  11. Homework • P449 #1, 3 – 9a, 10

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