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Week8-2up - Key DRAW PICTURES Tables to nd probabilities...

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STA 2023 c B.Presnell & D.Wackerly - Lecture 13 156 Thought: Vital papers will demonstrate their vitality by moving from where you left them to where you can’t find them. Assignments : Today : P. 236 – 240 For tomorrow: Exercises 5.55 , 5.59 , 5.60 , 5.63 , 5.64 , 5.68 For Wednesday: P. 254 – 264, COMPUTER DEMO For Thursday: Exercises 6.1, 6.3, 6.4. 6.8 Last Time : Working with the Normal distribution Tables to find probabilities Key : DRAW PICTURES STA 2023 c B.Presnell & D.Wackerly - Lecture 13 157 Normal Approximation to the Binomial Distribution p. 236 – 240 Suppose bin has a binomial distribution Sample size : Probability of a “success” : (p. 185, Chpt. 4) If is “large” the probabilities involving can be approximated with probabilities based on a Normal distribution with mean and standard deviation
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STA 2023 c B.Presnell & D.Wackerly - Lecture 13 158 See Figure 5.18, p. 237 9 8 7 6 5 4 3 2 1 0 10 Normal Density μ=5,σ=1.581 Binomial Histogram n = 10, p = .5 P(3 < x < 5) STA 2023 c B.Presnell & D.Wackerly - Lecture 13 159 The .5’s are called corrections for continuity. The largest value of interest gets a little larger (by .5) to get to edge of box in the binomial histogram. Smallest values of interest gets a little smaller. Probabilities involving ’s obtained from table.
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STA 2023 c B.Presnell & D.Wackerly - Lecture 13 160 How “large” should be so that the normal approximation is “good enough” to use? (Figure 5.19, p. 238, p. 240) completely contained in the interval from to . 0
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