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.
See attachment for full question including the data.
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 ...
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.