Let X represent the number of events that are observed to occur in n units of time
Question:
a. Show that for a proportion 1 − α of all possible samples, X − zα/2σX < nλ < X + zα/2σX .
b. Let = X/n. Show that σ= σX /n.
c. Conclude that for a proportion 1−α of all possible samples, − zα/2σ< λ < + zα/2σ.
d. Use the fact that (( (/n to derive an expression for the level 100(1−α)% confidence interval for λ?
e. A 5 mL sample of a certain suspension is found to contain 300 particles. Let λ represent the mean number of particles per mL in the suspension. Find a 95% confidence interval for λ?
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