The operating lifetimes of a specific model of industrial drone batteries are normally distributed with mean μ\muμ hours and variance σ2\sigma^2σ2 hours2^22. Based on a single random sample of battery lifetimes, a 99%99\%99% confidence interval for μ\muμ was calculated to be:
(18.22,21.78) (18.22, 21.78) (18.22,21.78)Using the same sample data,
determine a 95%95\%95% confidence interval for μ\muμ.
Six independent random samples are taken from the population, and a 95%95\%95% confidence interval is constructed for each sample.
Calculate the probability that exactly 5 of these 6 intervals 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.