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4 marksBinomial Distribution

CAPE Applied Mathematics Unit 1 · 2010 · Paper 2 · Question 4(a)(ii)

The probability of rain on any day in September is 0.55, independently from day to day.

What is the probability that it will rain on exactly 3 days in the next 7 days?

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Other parts of this question

  1. 4(a)(i)How many days in September is it expected to rain?[2 marks]
  2. 4(a)(iii)What is the probability that it will rain on the fourth, fifth, and sixth of September?[2 marks]
  3. 4(b)(i)Show that n = 15.[3 marks]
  4. 4(b)(ii)Hence calculate E(Y).[2 marks]
  5. 4(b)(iii)Calculate P(Y = 10).[3 marks]
  6. 4(c)(i)State TWO conditions that should exist for the normal distribution to be used as an approximation for the binomial distribution.[2 marks]
  7. 4(c)(ii)The probability that a pen is faulty is 0.06. In a box of 100 pens, what is the probability that at MOST 5 pens will be faulty?[7 marks]

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