Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
A machine randomly fills bags with sweets. The numbers of lemon and orange sweets in a bag have independent distributions $\text{Po}(3.7)$ and $\text{Po}(2.6)$ respectively.
One bag of sweets is selected at random.
(a)[2]
Find the probability that the number of lemon sweets in the bag is greater than $2$ but does not exceed $5$.
(b)[3]
Find the probability that the total number of lemon and orange sweets in the bag is less than $4$.
(c)[6]
Use approximating distributions to determine the probability that the total number of lemon sweets in the $10$ bags is less than the total number of orange sweets in the $10$ bags.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct application of Poisson probability $e^{-3.7}\left(\frac{3.7^3}{3!}+\frac{3.7^4}{4!}+\frac{3.7^5}{5!}\right)$.” …