The number of people joining an airport check-in queue in a period of 1 minute is a random variable with the distribution \(\mathrm{Po}(1.2)\).
Find the probability that, in a period of 4 minutes, at least 8 people join the queue.[1]
The probability that no more than 1 person joins the queue in a period of \(t\) seconds is \(0.7\). Find an equation for \(t\). Hence find the value of \(t\), giving your answer correct to the nearest whole number.[4]
The number of people leaving the same queue in a period of 1 minute is a random variable with the distribution \(\mathrm{Po}(1.8)\). At 0930 on a certain morning there are 35 people in the queue. Use appropriate approximations to find the probability that by 0945 there are at least 24 people in the queue, stating the parameters of any distributions that you use. (You may assume that the queue does not become empty during this period.)[5]
Explain why a Poisson model would probably not be valid if applied to a time period of several hours.[1]