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6 marksNormal Distribution

CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2 · Question 4(d)

The mass of a loaf of bread follows a normal distribution with mean 480 g and standard deviation 20 g. Calculate the probability that a randomly chosen loaf has mass between 465 g and 500 g.

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  1. 4(a)State THREE conditions required for a random variable to follow a binomial distribution.[3 marks]
  2. 4(b)(i)State with reason whether drawing three discs with replacement from a bag containing 4 yellow, 3 blue, and 2 white discs can be modelled by a binomial…[2 marks]
  3. 4(b)(ii)State with reason whether drawing three discs without replacement from a bag containing 5 yellow and 4 blue discs can be modelled by a binomial distribution.[2 marks]
  4. 4(b)(iii)State with reason whether drawing three discs with replacement from a bag containing 5 yellow and 4 blue discs can be modelled by a binomial distribution.[2 marks]
  5. 4(c)(i)For a group of 40 potential donors, calculate the expected number turned away due to tattoos.[2 marks]
  6. 4(c)(ii)a)For a random sample of 7 prospective donors, calculate the probability that none of them have tattoos.[3 marks]
  7. 4(c)(ii)b)For a random sample of 7 prospective donors, calculate the probability that exactly 3 of them have tattoos.[3 marks]
  8. 4(c)(ii)c)For a random sample of 7 prospective donors, calculate the probability that at least one of them has tattoos.[2 marks]

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