The masses of lithium-ion battery packs, B B\,B grams, are distributed such that B∼N(450,152)B \sim \text{N}(450, 15^2)B∼N(450,152).
Five battery packs are selected at random.
Calculate the probability that their total mass exceeds 2280 g.
The masses of industrial sensors, S S\,S grams, are such that S∼N(85,42)S \sim \text{N}(85, 4^2)S∼N(85,42).
Two sensors are selected at random.
Calculate the probability that the magnitude of the difference in their masses is more than 5 g.
The masses of protective housing units, H H\,H grams, are such that H∼N(1200,160)H \sim \text{N}(1200, 160)H∼N(1200,160).
The random variable A A\,A represents the total mass, in g, of a single housing unit packed with 10 sensors, where A A\,A and H H\,H are independent.
Calculate P(A>0.9H+950)P(A > 0.9H + 950)P(A>0.9H+950).