4 Chopped lettuce is sold in bags nominally containing 100 grams.
The weight, \(X\) grams, of chopped lettuce, delivered by the machine filling the bags, may be assumed to be normally distributed with mean \(\mu\) and standard deviation 4.

1. Assuming that \(\mu = 106\), determine the probability that a randomly selected bag of chopped lettuce:
   1. weighs less than 110 grams;
   2. is underweight.
2. Determine the minimum value of \(\mu\) so that at most 2 per cent of bags of chopped lettuce are underweight. Give your answer to one decimal place.
3. Boxes each contain 10 bags of chopped lettuce. The mean weight of a bag of chopped lettuce in a box is denoted by \(\bar { X }\). Given that \(\mu = 108.5\) :
   1. write down values for the mean and variance of \(\bar { X }\);
   2. determine the probability that \(\bar { X }\) exceeds 110 .