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Chapter 17 Probability Models
When dealing with a large population, it becomes impossible to use the binomial probability model. The numbers are simply too large for calculators to handle. But wait you can use the Normal model. The Normal model is a close enough approximation for a large enough number of trials.
Success/Failure Condition A Binomial model is approximately Normal if we expect at least 10 successes and 10 failures
np ≥ 10 and nq ≥ 10
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For a large sample size, the Normal model becomes a useful approximation.
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The Binomial model is discrete, giving probabilities for specific counts. The Normal models a continuous random variable that can take on any value.
Models for continuous random variables give probabilities for intervals of values. When we use the Normal model, we no longer calculate the probability that the random variable equals a particular value, but only that it lies between two values (think histogram). We obtain approximations with the Normal model, not exact values (Binomial model).
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689599.7 Rule
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28. More Arrows. The archer in Exercise 18 will be shooting 200 arrows in a large competition.
a. What are the mean and standard deviation of the number of bull'seyes she might get?
b. Is a Normal model appropriate here? Explain.
c. Use the 689599.7 Rule to describe the distribution of the number of bull'seyes she may get.
d. Would you be surprised if she made at most 140 bull'seyes? Explain
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29. Apples. An orchard owner knows that he'll have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples.
a. Describe an appropriate model for the number of cider apples that may come from that tree. Justify your model.
b. Find the probability there will be no more than a dozen cider apples.
c. Is it likely there will be more than 50 cider apples? Explain.
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HW p.403;27,30,31,33 ANS
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![High-Confidence, Low- Probability-of-Failure Screening January 11, 2014 RLGM? P[P[Failure|Eq]](https://img.pdfslide.net/doc/110x75/56649de85503460f94ae237b/high-confidence-low-probability-of-failure-screening-january-11-2014-rlgm.jpg)
