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.
(a) The mean number of hits in five hours is 100, so X~ Poisson(100). Therefore Xis approximately normal with mean 
The z-score of 95 is (95 ? 100) / 10 = ?0.50.
The area to the left of z= ?0.50 is 0.3085.
P(X ? 95) = 0.3085.
(b) No. More than 30% of five-hour periods will have 95 or fewer hits if the claim is true.
(c) No, because a total of 95 hits is not unusually small if the claim is true.
(d) The mean number of hits in five hours is 100, so ????~Poisson(100). Therefore ????is approximately normal with mean 
The z-score of 65 is (65 ? 100) / 10 = ?3.50.
The area to the left of z = ?3.50 is 0.0002.
P(X ? 65) = 0.0002.
(e) Yes. Only about 2 in 10,000 five-hour periods will have 65 or fewer hits if the claim is true.
(f) Yes, because a total of 65 hits is unusually small if the claim is true.
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