The lifespan of high-performance LED modules is normally distributed with an unknown mean, μ\muμ hours, and a known standard deviation, σ\sigmaσ hours. A random sample of 150 modules yields a 98% confidence interval for μ\muμ of
(2491.56,2508.44) (2491.56, 2508.44) (2491.56,2508.44)Using the confidence interval provided, test whether or not μ=2500\mu = 2500μ=2500. State your hypotheses clearly and the significance level used.
A second random sample of 200 modules had a mean lifespan of 2505 hours.
Calculate a 99% confidence interval for μ\muμ based on this second sample. You must show all steps in your working.
Using eight different random samples of 200 modules, eight 99% confidence intervals for μ\muμ are to be found.
Calculate the probability that at least 7 of these intervals will contain μ\muμ.