The masses of boxes of apples, A A\,A kg, are distributed such that A∼N(1.5,0.042)A \sim \text{N}(1.5, 0.04^2)A∼N(1.5,0.042).
Four boxes of apples are selected at random.
Calculate the probability that their total mass is less than 5.9 kg.
The masses of bags of pears, P P\,P kg, are such that P∼N(0.8,0.052)P \sim \text{N}(0.8, 0.05^2)P∼N(0.8,0.052).
Two bags of pears are selected at random.
Calculate the probability that the magnitude of the difference in their masses is more than 0.06 kg.
The masses of shipping crates, C C\,C kg, are such that C∼N(4.0,0.08)C \sim \text{N}(4.0, 0.08)C∼N(4.0,0.08).
The random variable G G\,G represents the total mass, in kg, of a single crate packed with 8 bags of pears. In P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0), C C\,C is the mass of a different, independently selected crate. Assume the crate and bag masses are independent.
Calculate P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0)