The popular "Snowy White" flour is sold in two types of packaging, namely standard and large. The weight of each standard packet of flour is a normal random variable with mean 70 g and standard deviation 10 g. The weight of each large packet of flour is a normal random variable with mean 150 g and standard deviation 25 g.

(i) Find the probability that the weight of a randomly chosen standard packet of "Snowy White" flour is at most 65 g. [2]

(ii) Find the probability that the total weight of four randomly chosen standard packets of "Snowy White" flour exceeds twice the weight of a randomly chosen large packet of "Snowy White" flour by less than 5 g. [3]

(iii) State an assumption needed for your calculation in part (ii).