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4 marksRandom Variables

CAPE Applied Mathematics Unit 1 · 2022 · Paper 2 · Question 4(b)(iv)

CompuFix repair times follow a normal distribution with mean 40 hours and standard deviation sigma hours.

If a repair time is exceptionally long, CompuFix pays compensation to the customer: US$250 if the repair time is between 50 and 55 hours. Determine the expected amount of compensation.

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  1. 4(a)(i)Determine the probability of getting at LEAST nine of the intended numbers when ten independent calls are made.[3 marks]
  2. 4(a)(ii)Calculate the mean number of intended numbers and the variance when ten independent calls are made.[2 marks]
  3. 4(a)(iii)Use a suitable approximation to find the probability of FAILING to get the intended number on at least 10 but NOT more than 20 of the calls.[6 marks]
  4. 4(b)(i)If it was found that 0.19% of the computers on a particular occasion had a repair time that was less than 24 hours, show that sigma = 5.5 (to one decimal…[4 marks]
  5. 4(b)(ii)Find the probability that the repair time is MORE than 35 hours.[3 marks]
  6. 4(b)(iii)CompuFix wishes to state in its advertisements that at LEAST 98% of all computers will be repaired in less than a certain number of hours. Determine the…[3 marks]

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