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.
