The lifespan of a certain type of industrial LED, measured in hours, is assumed to follow a normal distribution with mean μ\muμ and variance σ2\sigma^2σ2. Based on data from a single random sample of these LEDs, a 99%99\%99% confidence interval for μ\muμ was calculated to be:
(11484.84,12515.16) (11484.84, 12515.16) (11484.84,12515.16)Using the data from this same sample:
Determine a 95%95\%95% confidence interval for μ\muμ.
Eight independent random samples are subsequently collected, and a 95%95\%95% confidence interval for μ\muμ is constructed for each of these eight samples.
Calculate the probability that exactly 7 of these 8 intervals will contain the true population mean μ\muμ.
