Paper 1 · November 2018 · Poisson Distribution

Under which conditions can the Poisson distribution be used as an approximation to the Binomial distribution?

Awhen

n

is large and

p

is small

Bwhen

n

is large and

p

is close to 1

Cwhen

n

and

p

are both large

Dwhen

n

is small and

p

is close to 0.5

Explanation

The Poisson approximation to the Binomial works well when the number of trials n is large and the probability of success p is small, so that the mean np remains a moderate, finite value; the Normal approximation is preferred instead when p is close to 0.5.

Derived from ZIMSEC Statistics Paper 1, November 2018, Q6

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