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1 markBinomial Distribution

CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2 · Question 4(a)(iv)

For each of the given random variables, state whether or not it can be modelled by a binomial distribution.

A bag contains 8 white and 12 red marbles, all identical except for colour. A marble is taken from the bag and placed in another bag. This process is done 6 times. X is the number of red marbles taken.

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  1. 4(a)(i)A card is taken from an ordinary pack of cards, its suite (Ace, Spade, Diamond, Heart) noted, and it is replaced in the pack. The process is repeated 12 times.…[1 mark]
  2. 4(a)(ii)A fair die is tossed. This process is repeated a number of times. X is the number of throws of the fair die until a 6 is obtained.[1 mark]
  3. 4(a)(iii)10 seeds are planted. The probability of a seed germinating is 0.8. X is the number of seeds that germinate.[1 mark]
  4. 4(b)(i)Determine the expected number of patients in the sample who would not keep their follow-up appointment.[2 marks]
  5. 4(b)(ii)a)Calculate the probability that exactly 4 patients did not keep the follow-up appointment.[3 marks]
  6. 4(b)(ii)b)Calculate the probability that at most 2 patients did not keep their follow-up appointment.[3 marks]
  7. 4(c)The random variable X has a normal distribution with mean 12 and variance 4. Find the constant c such that P(X < c) = 0.9332.[3 marks]
  8. 4(d)(i)What is the probability that a rod selected at random will measure more than 65 centimetres?[5 marks]
  9. 4(d)(ii)Rods that are less than 54 centimetres are cut and sold as a smaller length. What percentage of rods will have to be cut?[5 marks]

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