Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

The count of accidents on one particular road follows a Poisson distribution with mean $0.4$ per $50$-day period.
(a)[3]

Determine the chance that fewer than $3$ accidents occur in a year ($365$ days).

(b)[4]

The chance that no accidents happen over a period of $n$ days is above $0.95$. Find the largest possible value of $n$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Working out $\lambda = 0.4 \times 365 \div 50 = 2.92$.

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