A manufacturer produces high-precision glass panels for microchip housing.
The thickness, T T\,T mm, of a panel follows a normal distribution with unknown mean μ \mu\,μ and a known standard deviation of 0.08 mm.
A batch of 64 panels is selected for quality control. The sum of the thicknesses of these 64 panels is recorded as 783.36 mm.
Determine a 95% confidence interval for the mean thickness, μ\muμ, of the panels. (4)
Explain why the Central Limit Theorem was not required for the calculation in part (a). (1)
The manufacturer claims that the process is calibrated to a mean thickness of 12.27 mm.
Using your result from part (a), assess whether the sample data supports this claim. (2)
The mass, M M\,M grams, of adhesive resin applied to the frames follows a normal distribution with mean 450 g and standard deviation 15 g.
A shipment of 9 resin containers is examined.
Calculate the probability that the mean mass of resin in these 9 containers is less than 442 g. (3)