Assuming the owner is right, determine the probability that there are at least $4$ hits in a $10$-minute interval.
Use an appropriate approximating distribution to determine the probability that there are fewer than $40$ hits in a $3$-hour interval.
Assume the owner is correct.
A friend also accepts that the website gets, on average, $0.3$ hits per minute. Even so, she observes that the number of hits in the day-time ($9.00\ \text{am}$ to $9.00\ \text{pm}$) is usually about twice the number of hits in the night-time ($9.00\ \text{pm}$ to $9.00\ \text{am}$).
Explain why this observation contradicts the owner’s belief that the number of hits per minute follows a Poisson distribution.
State separate Poisson distributions that could reasonably model the number of hits during the day-time and during the night-time.