(a(i))[3]
Assuming the owner is right, determine the probability of at least $4$ hits in a $10$-minute interval.
(a(ii))[4]
Use a suitable approximating distribution to determine the chance of fewer than $40$ hits in a $3$-hour interval.
(b(i))[1]
A friend accepts that the website averages $0.3$ hits per minute. However, she observes that the number of hits in the daytime ($9.00\,\text{am}$ to $9.00\,\text{pm}$) is usually about double the number in the night-time ($9.00\,\text{pm}$ to $9.00\,\text{am}$). Explain why this conflicts with the owner’s belief that the number of hits per minute follows a Poisson distribution.
(b(ii))[2]
State separate Poisson distributions that could be appropriate models for the number of hits in the daytime and in the night-time.