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5 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2013 · Paper 2 · Question 4(a)(iii)

Highway accidents occur at an average rate of one per week.

A year consists of approximately thirteen 4-week periods. Determine the probability that in a particular year there are exactly eleven periods during which AT LEAST 4 accidents occur.

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Other parts of this question

  1. 4(a)(i)Determine the probability of exactly 2 accidents in any one-week period.[3 marks]
  2. 4(a)(ii)Given that on average 4 accidents occur in a 4-week period, show that the probability of at least 4 accidents in a 4-week period is 0.567 to 3 decimal places.[4 marks]
  3. 4(b)With the use of another justified probability distribution function as an approximation, determine the probability that a box contains AT MOST two defective…[6 marks]
  4. 4(c)(i)Determine the value of the constant k.[3 marks]
  5. 4(c)(ii)Determine the value of t such that P(X > t) = \frac{1}{4}.[4 marks]

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