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2015 NYJC P2 Q7 [Modified]

2015 NYJC P2 Q7 [Modified]

In a sample of \(60\) calls received by a call service centre, the average number of complaints is \(4.8\). Let \(C\) be the number of complaints in the sample of \(60\) calls.

  1. Give a reason why \(C\) may not follow a binomial distribution.
  2. Assuming a binomial distribution for \(C\), find the probability that at least one-tenth of the calls are complaints.

Solution:

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Answer:(i) Calls may be dependent, for example because of a common service problem. (ii) \(C\sim B(60,0.08)\), \(P(C\ge6)\approx0.347\).

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