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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.