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)
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.