- A call centre routes incoming telephone calls to agents who have specialist knowledge to deal with the call. The probability of a caller, chosen at random, being connected to the wrong agent is p.
The probability of at least 1 call in 5 consecutive calls being connected to the wrong agent is 0.049
The call centre receives 1000 calls each day.
- Find the mean and variance of the number of wrongly connected calls a day.
- Use a Poisson approximation to find, to 3 decimal places, the probability that more than 6 calls each day are connected to the wrong agent.
- Explain why the approximation used in part (b) is valid.
The probability that more than 6 calls each day are connected to the wrong agent using the binomial distribution is 0.8711 to 4 decimal places.
- Comment on the accuracy of your answer in part (b).