A quality control technician monitors the viscosity, vvv centipoise (cP), of a batch of synthetic lubricant. The measured viscosity, VVV cP, follows a normal distribution with mean μ\muμ cP and standard deviation 3.23.23.2 cP.
Find the probability that a single measurement of the viscosity is within 2.42.42.4 cP of the mean μ\muμ.
The technician takes a random sample of 64 independent measurements.
Determine the probability that the sample mean of these 64 results, Vˉ\bar{V}Vˉ, is within 0.60.60.6 cP of μ\muμ.
Given that the mean of these 64 measurements is 412.5412.5412.5 cP, calculate a 95%95\%95% confidence interval for μ\muμ, giving your limits to three decimal places.
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.