In a bioreactor, the dissolved oxygen concentration CCC (mg/L) follows a normal distribution C∼N(μ,σ2)C \sim \mathrm{N}(\mu, \sigma^2)C∼N(μ,σ2). Based on a random sample of measurements, an 80% confidence interval for μ \mu\,μ is determined to be (18.0155,18.7845)(18.0155, 18.7845)(18.0155,18.7845).
Determine a 95% confidence interval for the mean dissolved oxygen concentration μ\muμ.
The total oxygen content in a specific tank volume is given by the linear relationship Q=2.5C+4Q = 2.5C + 4Q=2.5C+4. Using your answer to part (a), calculate a 95% confidence interval for the mean oxygen content μQ\mu_QμQ.
Five independent random samples are collected from different bioreactors with the same mean μ\muμ. A 95% confidence interval for μ \mu\,μ is calculated for each sample. Find the probability that at least four of these five intervals will capture the true value of μ\muμ.
