The electrical resistance of a batch of specialized superconducting components, R R\,R ohms, follows a normal distribution such that R∼N(μ,0.82)R \sim \text{N}(\mu, 0.8^2)R∼N(μ,0.82).
It is known that 20% of these components have a resistance exceeding 100.5 ohms. Determine the value of μ \mu\,μ to the nearest 0.1 ohm.
A technician randomly selects 12 components from the batch for testing.
Find the probability that fewer than 2 of these components have a resistance exceeding 100.5 ohms.
A large-scale circuit assembly requires 150 of these components selected at random.
Using a suitable approximation, find the probability that more than 35 of these components have a resistance exceeding 100.5 ohms.