Square the coefficient of a two-packet total and retain both tails

Fettuccine packet mass is normal with mean 450 g and standard deviation σg.10% weigh at most 437 g.

(i) Find σ.2 marks

Spaghetti packet masses follow $N(500,9.2^2)$. Thomas buys six spaghetti packets and two fettuccine packets.

(ii) Find the probability that the total spaghetti mass differs from twice the two-packet fettuccine total by at least 1250 g.3 marks

(iii) State an assumption needed in(ii).1 mark