Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
During winter in one mountainous area, the chance that more than $20\text{ cm}$ of snow falls on a given day is $0.21$.
(i)[3]
Determine the chance that, within any winter $7$-day interval, fewer than $5$ days experience more than $20\text{ cm}$ of snow.
(ii)[4]
For $4$ randomly selected $7$-day periods in winter, determine the probability that exactly $3$ of them will include at least $1$ day with more than $20\text{ cm}$ of snow falling.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Work with $P(X<5)=1-P(5,6,7)$, or another binomial expression that uses powers $\ge7$ and probabilities $\ge1$, and includes ${}^7C_r$” …