Standard +0.3 This is a multi-part question covering standard S2 Poisson distribution content. Part (a) requires simple recall of a condition (λ ≥ 10), parts (b)-(d) are routine Poisson calculations, and part (e) applies the normal approximation in a straightforward way. While comprehensive, all parts follow textbook procedures with no novel problem-solving required, making it slightly easier than average.
3. (a) State the condition under which the normal distribution may be used as an approximation to the Poisson distribution.
The number of reported first aid incidents per week at an airport terminal has a Poisson distribution with mean 3.5
(b) Find the modal number of reported first aid incidents in a randomly selected week. Justify your answer.
The random variable \(X\) represents the number of reported first aid incidents at this airport terminal in the next 2 weeks.
(c) Find \(\mathrm { P } ( X > 5 )\)
(d) Given that there were exactly 6 reported first aid incidents in a 2 week period, find the probability that exactly 4 were reported in the first week.
(e) Using a suitable approximation, find the probability that in the next 40 weeks there will be at least 120 reported first aid incidents.
3. (a) State the condition under which the normal distribution may be used as an approximation to the Poisson distribution.
The number of reported first aid incidents per week at an airport terminal has a Poisson distribution with mean 3.5\\
(b) Find the modal number of reported first aid incidents in a randomly selected week. Justify your answer.
The random variable $X$ represents the number of reported first aid incidents at this airport terminal in the next 2 weeks.\\
(c) Find $\mathrm { P } ( X > 5 )$\\
(d) Given that there were exactly 6 reported first aid incidents in a 2 week period, find the probability that exactly 4 were reported in the first week.\\
(e) Using a suitable approximation, find the probability that in the next 40 weeks there will be at least 120 reported first aid incidents.\\
\hfill \mbox{\textit{Edexcel S2 2017 Q3 [16]}}