Let X represent the number of events that are observed to occur in n units of time or space, and assume X ~ Poisson 
, where ? is the mean number of events that occur in one unit of time or space. Assume X is large, so that 
. Follow steps (a) through (d) to derive a level 100(1 – ?)% confidence interval for ? . Then in part (e), you are asked to apply the result found in part (d).
a. Show that for a proportion 1 – ? of all possible samples,
b.
c. Conclude that for a proportion 1 – ? of all possible samples 
d. Use the fact that 
to derive an expression for the level 100(1 – ?)% confidence interval for ? .
e. A 5 mL sample of a certain suspension is found to contain 300 particles. Let ? represent the mean number of particles per mL in the suspension. Find a 95% confidence interval for ?.
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