The operating lifetimes of a specific model of industrial drone batteries are normally distributed with mean μ\muμ hours and variance σ2\sigma^2σ2 hours2^22. Based on a single random sample of battery lifetimes, a 99%99\%99% confidence interval for μ\muμ was calculated to be:
(18.22,21.78) (18.22, 21.78) (18.22,21.78)Using the same sample data,
determine a 95%95\%95% confidence interval for μ\muμ.
Six independent random samples are taken from the population, and a 95%95\%95% confidence interval is constructed for each sample.
Calculate the probability that exactly 5 of these 6 intervals contain the true population mean μ\muμ.
