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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.