A botanical research lab collects soil samples for analysis. The weight of an individual soil sample, SSS, is modelled by a normal distribution with mean 4.12 kg and standard deviation 0.15 kg.
Find the probability that the weights of two randomly selected soil samples differ by more than 0.25 kg.
Soil samples are grouped and placed into storage bins for transport. The weight of an empty storage bin, BBB, is modelled by a normal distribution with mean 15.4 kg and standard deviation 1.40 kg.
Each fully loaded storage bin contains 30 soil samples.
Find the probability that the total weight of a randomly selected fully loaded storage bin is less than 136.5 kg.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.