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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.