Cornflakes are packed in boxes and the boxes are then packed into cartons. Each carton contains 10 boxes. The weights of the boxes of cornflakes are normally distributed with a mean of 500g and a standard deviation of 25g. The weights of the empty cartons are also normally distributed with μ = 2000g and σ = 100g.
a. Calculate the mean and variance for a full carton.
b. 90% of full cartons lie below a certain weight (x). Calculate the value of x.