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Constructing approx confidence intervals for a Piosson r.v.

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It was suggested that the number of particles in a randomly selected interval might follow a Poisson distribution. Assuming a Poisson distribution to be an appropriate model for the data, use two methods to find an approximate 95% confidence interval for the mean of this distribution.

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Solution Summary

A step-by-step solution is provided in the Word attachment. It is shown how to construct an approximate 95% confidence interval for a Poisson random variable. The question asks for 2 methods. A complete solution is provided for 1 method and a hint is provided for method number 2.

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To find a confidence interval, we first need to find the mean and the standard deviation of this sample.

To find the mean - we just sum up the multiplications of the number times frequency, and then divide by the total frequency. To illustrate...

Xbar = [57(0) + 203(1) + ... + 2(12)]/2612
Xbar = 3.88.

Next, we find the standard deviation. Remember, for ...

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