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3 marksBinomial Distribution

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

A dentist found that 30% of new patients do not keep their follow-up appointments. A random sample of 15 patient records is selected.

Calculate the probability that exactly 4 patients did not keep the follow-up appointment.

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Other parts of this question

  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(a)(iv)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…[1 mark]
  5. 4(b)(i)Determine the expected number of patients in the sample who would not keep their follow-up appointment.[2 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]

More practice: the rest of this paper · more Binomial Distribution questions · all CAPE Applied Mathematics Unit 1 past papers