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.
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.