I need help some help with the below problem and would appreciate very much if can offer some help.
Fish and prawns are sold by weight. The masses, in kg, of fish and prawns are modelled as having independent normal distributions with means and standard deviations as shown in the table.
Fish : Mean mass = 2.2 , Standard deviation= 0.5
Prawns : Mean mass = 10.5 Standard deviation= 2.1
Fish are sold at $3 per kg and prawns at $5 per kg.
(i) Find the probability that a randomly chosen fish has a selling price exceeding $7. (0.395)
(ii) Find the probability of the event that both a randomly chosen fish has a selling price exceeding $7 and a randomly chosen prawn has a selling price exceeding $55. (0.160)
(iii) Find the probability that the total selling price of a randomly chosen fish and a randomly chosen prawn is more than $62. (0.392)
(iv) Explain why the answer to part (iii) is greater than the answer to part (ii).