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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.