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.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.