Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

On average, it is known that 1 in 300 flowers of a particular kind are white. A random sample of 200 flowers of that kind is then selected.
(a)[3]

Apply a suitable approximating distribution to determine the probability that more than 1 flower in the sample is white.

(b)[1]

Give a justification for the approximating distribution used in part (a).

(c)[3]

The probability that a randomly selected flower of another kind is white is $0.02$. A random sample of 150 of these flowers is then selected. Use an appropriate approximating distribution to find the probability that the total number of white flowers in the two samples is less than $4$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Poisson distribution with the correct mean $\lambda = \frac{2}{3}$ shown or understood.

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