A hint to get started
Apply prices after adding independent masses
Melons cost $1.50 per kilogram and their masses are normal with mean 0.8 kg and standard deviation 0.1 kg. Pumpkins cost $0.50 per kilogram and their masses are normal with mean 1.2 kg and standard deviation 0.2 kg. Find the probability that the total price of 5 randomly chosen melons and 3 randomly chosen pumpkins exceeds $8.
[N2002/II/28]
CJC · Lecture · Example 9
There are eight distinct fruit observations, but the prices scale each group’s total mass.
Price per kilogram multiplies a standard deviation directly and a variance by its square.