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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
