Scale fruit masses before combining independent prices

Durians cost 7 dollars per kg; a durian’s mass is normal with mean 1.5 kg and standard deviation 0.2 kg. Mangoes are sold in bags of 5 at 2 dollars per kg. One mango’s mass is normal with mean 0.4 kg and standard deviation 0.05 kg. Fruit masses are independent; empty bag mass is negligible.

(i) Find the probability that a random bag of mangoes costs more than 4.20 dollars.3 marks

(ii) Find the probability that both a random durian costs more than 10 dollars and a random mango bag more than 4.20 dollars.3 marks

(iii) Find the probability that 2 durians and 3 mango bags cost less than 33.50 dollars in total.5 marks