The lifespan of a certain type of industrial LED, measured in hours, is assumed to follow a normal distribution with mean μ\muμ and variance σ2\sigma^2σ2. Based on data from a single random sample of these LEDs, a 99%99\%99% confidence interval for μ\muμ was calculated to be:
(11484.84,12515.16) (11484.84, 12515.16) (11484.84,12515.16)Using the data from this same sample:
Determine a 95%95\%95% confidence interval for μ\muμ.
Eight independent random samples are subsequently collected, and a 95%95\%95% confidence interval for μ\muμ is constructed for each of these eight samples.
Calculate the probability that exactly 7 of these 8 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.