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.
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.