N2007 P2 Q8

Chickens and turkeys are sold by weight. The masses, in kg, of chickens and turkeys are modelled as having independent normal distributions with means and standard deviations as shown in the table.

Chickens are sold at $3 per kg and turkeys at $5 per kg.

1. Find the probability that a randomly chosen chicken has a selling price exceeding $7.[2]
2. Find the probability of the event that both a randomly chosen chicken has a selling price exceeding $7 and a randomly chosen turkey has a selling price exceeding $55.[3]
3. Find the probability that the total selling price of a randomly chosen chicken and a randomly chosen turkey is more than $62.[4]
4. Explain why the answer to part (iii) is greater than the answer to part (ii).[1]