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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.