A factory manufactures steel rods with length L L\,L cm, where L∼N(μ,σ2)L \sim \mathrm{N}(\mu, \sigma^2)L∼N(μ,σ2). From a random sample of rods, an 80% confidence interval for μ \mu\,μ is calculated as (74.36,75.64)(74.36, 75.64)(74.36,75.64).
Find a 95% confidence interval for μ\muμ.
Using the formula for the volume of a rod V=10LV = 10LV=10L, find a 95% confidence interval for the mean volume of these rods.
If four independent random samples are taken and a 95% confidence interval for μ \mu\,μ is calculated for each, find the probability that at least three of these intervals will contain the true value of μ\muμ.
