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7 marksNormal Distribution

CAPE Applied Mathematics Unit 1 · 2021 · Paper 2 · Question 4(a)(vi)

A credit union found 25% of customers do not make monthly payments on time. A random sample of 20 customers is taken.

For a sample of 100 customers, use a suitable approximation to determine the probability that no more than 35 customers make their monthly payments on time, stating all your assumptions.

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Other parts of this question

  1. 4(a)(i)Identify the distribution that may be used to model this situation.[1 mark]
  2. 4(a)(ii)State the parameters of the distribution.[1 mark]
  3. 4(a)(iii)Determine the expected number of customers in the sample who do not make their monthly payments on time.[2 marks]
  4. 4(a)(iv)Calculate the probability that exactly 5 customers do not make their monthly payments on time.[2 marks]
  5. 4(a)(v)Calculate the probability that at most 3 customers do not make their monthly payments on time.[4 marks]
  6. 4(b)(i)Determine the probability that a javelin selected at random will measure more than 255 cm.[4 marks]
  7. 4(b)(ii)Javelins less than 220 cm are cut and sold as fence posts. Calculate the percentage of javelins that will have to be cut and sold as fence posts.[4 marks]

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