Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
A certain kind of plant usually has three leaves. However, it is known that, on average, $1$ in $10\,000$ of these plants has four leaves, and plants with four leaves are described as ‘lucky’. Let $X$ represent the number of lucky plants in a random sample of $25\,000$ plants.
(a)[2]
State, with a justification, an approximating distribution for $X$, and include the values of any parameters.
(b)[2]
Find the value of $P(X \le 3)$.
(c)[2]
Given that $P(X = k) = 2P(X = k + 1)$, find the value of $k$.
(d)[3]
The number of lucky plants in a random sample of $n$ plants, with $n$ large, is denoted by $Y$. Given that $P(Y \ge 1) = 0.963$, correct to $3$ significant figures, use an appropriate approximating distribution to find the value of $n$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A Poisson distribution with mean $\lambda = 2.5$” …