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STA_Notes_9.24.07 - STA Class To find Binomial Random...

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STA Class 13:10:57 To find Binomial Random Variable Probabilities o 1. Use methods from Ch 3 o 2. Use Binomial Point Probability Distribution Fig 4.3-3 n = number of trials p = prob. Of success q = prob. Of failure Three Children example o Find the probability that none of the 3 children get the disease Fig 4.3-4 o Find the prob. That exactly one of the 3 children get the disease Fig. 4.3-5 Solving Binomial Probabilities o Very small n (1-4) calculate distribution and probabilities using formula. o Binomial tables in back of book can be used for values of n = 5, 6, 7, 8, 9, 10, 15, 20, and 25 (pages 885 – 888) o Use Normal approximation for large n (section 5.5) To use Binomial Tables: o X is binomial with n = 15 and p = .3 o Tables give cumulative probabilities . o Find the probability that x is: Fig 4.3-6 1. At most 3 (what values?) = .297 2. At least 3 = .873 3. Exactly 3 = .17 4. Less than 3 = .127 5. Exceeds 3 = .703
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STA Class 13:10:57 Mean and variance of a binomial random variable o µ = µ p, σ² = npq o
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