Condition on the total length before interpreting two short pickles

Peter Piper guarantees every pickle is at least 8 cm long; his bottles hold pickles of at most 10.5 cm. Pickle length is normal with mean 9 cm and standard deviation 0.8 cm.

(i) Find the probability a random pickle must be discarded because(a) it is below the guaranteed length 1 mark or (b) it does not fit the bottle.1 mark

(ii) He wants to discard no more than 5% of pickles. Comment on whether this is possible.1 mark

(iii) Find the probability that both of two randomly selected pickles fail the guarantee, given that their total length is below 16 cm.3 marks