Further Mathematics · Pearson Edexcel 9FM0 · Option FS1 · Topic 2

Poisson and binomial distributions

The Poisson distribution for counts of random events, and how it combines with and approximates the binomial distribution.

3 sub-topics
Taught in Year 12
53 practice questions
3 animated lessons

Practice questions (53) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

2.1The Poisson distributionY12
2.2Mean and variance of binomial and PoissonY12
2.3Poisson approximation to the binomialY12

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Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 53 questions in this topic, free, no account needed.

Poisson and binomial distributions

Easy

The Poisson distribution · Year 12 · 1 mark

$X \sim \mathrm{Po}(3.0)$ . What is $\mathrm{P}(X = 0)$ ?
(1)

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$\mathrm{P}(X = 0)$ ${}= \mathrm{e}^{-\lambda}$ . $C$ : $0.0498$

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Poisson and binomial distributions

Medium

The Poisson distribution · Year 12 · 7 marks

Calls arrive at a help desk at random, at an average rate of 1.5 per hour.

(a)
Give two reasons why a Poisson distribution may be a suitable model for the number of calls in an hour.
(2)
(b)
Find the probability that at least 3 calls arrive in a 3-hour period.
(3)
(c)
Find the probability that at least one call arrives in each of three separate one-hour periods.
(2)

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Part (a)2 marks

Calls arrive singly and independently.
Calls arrive at a constant average rate.

Part (b)3 marks

Scale the rate to the interval. $Y \sim \mathrm{Po}(4.5)$
$\mathrm{P}(Y \geq 3)$ ${}= 1 - \mathrm{P}(Y \leq 2)$
$= 0.8264$

Part (c)2 marks

Independent hours. $\left(1 - \mathrm{e}^{-1.5}\right)^3$
$= 0.4689$

Total7

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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