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4 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2017 · Paper 2 · Question 4(a)

Rectangular metal sheets have an average of 2 blisters for every 15\text{ m}^2 of metal, modelled by a Poisson distribution.

Determine, to 3 significant figures, the probability that a piece of metal 15\text{ m}^2 will contain at most three blisters.

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  1. 4(b)Justifying the use of a suitable approximation, calculate the probability that at least 2 customers intend to pay their arrears.[5 marks]
  2. 4(c)(i)State clearly the distribution which can be used to approximate the Poisson distribution.[1 mark]
  3. 4(c)(ii)Calculate the probability that in one hour less than 32 calls are received.[4 marks]
  4. 4(c)(iii)Calculate the probability that in one hour between 31 and 39 calls are received.[4 marks]
  5. 4(d)(i)Complete the table by giving the expected number of persons preferring each brand, assuming that each brand is equally likely to be preferred.[1 mark]
  6. 4(d)(ii)Perform a \chi^2 goodness-of-fit test at the 1% significance level to determine whether a uniform distribution fits the tea-drinking preference of the 250…[6 marks]

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