The volume of a specialty chemical, V V\,V millilitres, dispensed into vials by an automated lab pump is normally distributed with mean 50.0 ml and standard deviation 0.4 ml.
(i) State the value of P(V≠50.0)P(V \neq 50.0)P(V=50.0).
(ii) Calculate the probability that a randomly selected vial contains between 49.3 ml and 50.6 ml of the chemical.
Determine the volume that is exceeded by 95% of the vials dispensed by this pump.
A different model of pump, the 'Beta-Flow', dispenses a volume W W\,W millilitres which is normally distributed with mean 45.0 ml and an unknown standard deviation σ\sigmaσ. Given that 8% of the vials dispensed by the Beta-Flow pump contain more than 46.2 ml, find the value of σ\sigmaσ, giving your answer to three significant figures.
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.