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Unformatted text preview: 6-6 Normal as Approximation to BinomialThis section describes another interesting application of the normal distribution. In section 5-3, you learned how to find binomial probabilities. For instance, if a surgical procedure has an 85% chance of success and a doctor performs the procedure on 10 patients, it is easy to find the probability of exactly two successful surgeries. But what if the doctor performs the surgical procedure on 150 patients and you want to find the probability of fewer than 100 successful surgeries? To do this using the techniques described in section 5-3, you would have to use the binomial formula 100 times and find the sum of the resulting probabilities. This approach is not practical, of course. A better approach is to use a normal distribution to approximate the binomial distribution. Normal Approximation to a Binomial Distribution If np, then the binomial random variable x is approximately normally distributed, with mean =npand standard deviation = . Ex (1) Decide whether you can use the normal distribution to approximate x, the number of people who reply yes. If you can, find the mean and standard deviation. If you cannot, explain why....
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