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 \(P(X \leq 95)\)?

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 \(P(X \leq 65)\)?

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.

Equation transcription:

Text transcription:

P(X \leq 95)

P(X \leq 65)

Solution

Step 1 of 7

Here we have to find the poisson probabilities for the given conditions

Let X be the no. of hits in five hours

No. of hits per hour =20

No. of hits per 5 hours=20(5)=100

Here XPoisson (100)

So =100

The value is very large the distribution is converted to normal distribution

So XN(100,100)

Here mean =100

Standard deviation =

=10