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Using the Normal Approximation to the Binomial

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According to study done by Nick Wilson of Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing was 0.267. Suppose you sit on a mall bench and observe 200 people pass by as they sneeze.

1) Use the normal approximation to the binomial to find the probability of observing less than 40 people that don't cover while sneezing.

2) Find the actual probability of observing less than 40 people that don't cover their nose while sneezing using the binomial. How close are the two probabilities?

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This solution provides a step-by-step solution to using the normal approximation for finding probabilities.

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Determining if the normal approximation to the binomial distribution should be used.

Determine if the normal approximation to the binomial distribution could be used for the following problems:

A.) A study found that 1% of Social Security recipients are too young to vote. 800 Social Security recipients are randomly selected.

B.) A study found that 30% of the people in a community use the library in one year. 15 people from the community were selected.

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