6. A geologist is analysing the size of quartz crystals in a sample of granite. She estimates that the longest diameter of \(75 \%\) of the crystals is greater than 2 mm , but only \(10 \%\) of the crystals have a longest diameter of more than 6 mm . The geologist believes that the distribution of the longest diameters of the quartz crystals can be modelled by a normal distribution.

1. Find the mean and variance of this normal distribution. The geologist also estimated that only \(2 \%\) of the longest diameters were smaller than 1 mm .
2. Calculate the corresponding percentage that would be predicted by a normal distribution with the parameters you calculated in part (a).
3. Hence, comment on the suitability of the normal distribution as a model in this situation.
   (2 marks)