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.
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.