The mass, in grams, of a Chocolate Delight cake is normally distributed with mean 20 g and

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The mass, in grams, of a Chocolate Delight cake is normally distributed with mean 20 g and standard deviation 2 g. The cakes are sold in packets of six and the mass of the packing material is normally distributed with a mean of 30 g and a standard deviation of 4 g.

(a) Find the probability that the mass of six cakes is less than 110 g.

(b) Find the probability that the total mass of a packet containing six cakes is (i) more than 162 g. (ii) less that 137 g (iii) between 140 g and 153 g.

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