The lifespan of high-performance LED modules is normally distributed with an unknown mean, μ\muμ hours, and a known standard deviation, σ\sigmaσ hours. A random sample of 150 modules yields a 98% confidence interval for μ\muμ of
(2491.56,2508.44) (2491.56, 2508.44) (2491.56,2508.44)Using the confidence interval provided, test whether or not μ=2500\mu = 2500μ=2500. State your hypotheses clearly and the significance level used.
A second random sample of 200 modules had a mean lifespan of 2505 hours.
Calculate a 99% confidence interval for μ\muμ based on this second sample. You must show all steps in your working.
Using eight different random samples of 200 modules, eight 99% confidence intervals for μ\muμ are to be found.
Calculate the probability that at least 7 of these intervals will contain 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.