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 (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.