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.
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.