Mathematics 9709/72 — October/November 2019

Cambridge A-Level · Probability & Statistics 2 · worked solutions for every part, with the mark scheme

questions

marks

minutes

Topics The Poisson Distribution · Sampling and Estimation · Hypothesis Tests · Continuous Random Variables · Linear Combinations of Random Variables

Q1The Poisson DistributionFree sample

On average, 1 in 150 components made by a certain machine are faulty. The random variable $X$ denotes the number of faulty components in a random sample of 500 components.

(i)

Describe fully the distribution of $X$ .

(ii)

State a suitable approximating distribution for $X$ , giving a justification for your choice.

(iii)

Use your approximating distribution to find the probability that the sample will include at least 3 faulty components.

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5 more questions

Q2Sampling and Estimation · Hypothesis Tests8M
Q3Sampling and Estimation7M
Q4Continuous Random Variables9M
Q5Linear Combinations of Random Variables9M
Q6Hypothesis Tests · The Poisson Distribution10M

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