3. A call-centre dealing with complaints collected data on how long customers had to wait before an operator was free to take their call. The lower quartile of the data was 12.7 minutes and the interquartile range was 5.8 minutes.

1. Find the value of the upper quartile of the data. It is suggested that a normal distribution could be used to model the waiting time.
2. Calculate correct to 3 significant figures the mean and variance of this normal distribution based on the values of the quartiles.
   (8 marks)
   The actual mean and variance of the data were 15.3 minutes and 20.1 minutes \(^ { 2 }\) respectively.
3. Comment on the suitability of the model.
   (2 marks)