Someone claims that the number of hits on his website has a Poisson distribution with mean 20 per hour. Let X be the number of hits in five hours.

a. If the claim is true, what is P(X ≤ 95)?

b. Based on the answer to part (a), if the claim is true, is 95 hits in a five-hour time period an unusually small number?

c. If you observed 95 hits in a five-hour time period, would this be convincing evidence that the claim is false? Explain.

d. If the claim is true, what is P(X ≤ 65)?

e. Based on the answer to part (d), if the claim is true, is 65 hits in a five-hour time period an unusually small number?

f. If you observed 65 hits in a five-hour time period, would this be convincing evidence that the claim is false? Explain.