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Normal Approximation to Binomial Distribution

Normal Approximation to Binomial Distribution. Consider the binomial distribution with n trials, and probability of success is p This distribution is approximately normal if np > 5 and nq > 5. In this case it is approximated by a normal distribution with Mean = np and Variance = npq.

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Normal Approximation to Binomial Distribution

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  1. Normal Approximation to Binomial Distribution Consider the binomial distribution with n trials, and probability of success is p This distribution is approximately normal if • np > 5 and nq > 5. In this case it is approximated by a normal distribution with • Mean = np and Variance = npq

  2. This binomial distribution doesn’t look approximately normal (it is not bell shaped). Note np = 23.75 > 5 but nq = 1.25 < 5.

  3. The normal distribution is a good approximation: np = (25)(.7) = 17.5 > 5, nq = (25)(.3) = 7.5 > 5

  4. The normal is a good approximation: np = 32> 5 and nq = 8 > 5.

  5. The normal is a good approximation: np = 40> 5 and nq = 60 > 5.

  6. Ex: For the following distribution, estimate P(9 < r < 13) by • using the binomial probability formula directly; • using the normal approximation.

  7. Continuity Correction

  8. Overbooked Flights • Have you ever arrived at the airport and found that your flight was over booked?

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