A manufacturer of high-end drone batteries audits their production line for mass consistency. The random variable WWW, in grams, represents the mass of a battery cell when the machinery is calibrated to a target of 450.0 g. It is assumed that W∼N(μ,1.42)W \sim N(\mu, 1.4^2)W∼N(μ,1.42).
Five random cells were selected for testing, yielding the following masses:
448.2,449.1,451.5,447.8,448.9 448.2, \quad 449.1, \quad 451.5, \quad 447.8, \quad 448.9 448.2,449.1,451.5,447.8,448.9(i) Construct a 90% confidence interval for μ\muμ, giving your limits to 2 decimal places.
Using this interval, determine whether there is evidence to suggest the machinery requires recalibration.
In a subsequent quality control check involving a larger sample size nnn, the sample mean was found to be 449.2 g. Given that a 99% confidence interval for μ\muμ produced an upper limit that was strictly less than 450.0 g, find the minimum possible value of nnn.
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.