An industrial chemist is monitoring the reaction time, TTT seconds, for a specific catalytic process. It is assumed that TTT follows a normal distribution such that T∼N(μ,σ2)T \sim \operatorname{N}(\mu, \sigma^2)T∼N(μ,σ2).
A random sample of reaction times is recorded, and a 90%90\%90% confidence interval for μ\muμ is calculated as (141.05,148.95)(141.05, 148.95)(141.05,148.95).
Find, to 2 decimal places, the standard error of the mean.
Hence, or otherwise, determine a 99%99\%99% confidence interval for μ\muμ based on the same sample of reaction times.
Using six different random samples, six independent 99%99\%99% confidence intervals for μ\muμ are to be constructed.
Calculate the probability that at least 5 of these intervals will contain the true population mean μ\muμ.
