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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.