The pressure at which a specific type of hydraulic valve fails, measured in PSI, is normally distributed with mean μ \mu\,μ and standard deviation 12.5. Laboratory tests indicate that 12% of these valves fail at a pressure of less than 840 PSI. Find:
the value of μ\muμ, giving your answer to two decimal places.
the percentage of valves that are expected to withstand a pressure of more than 875 PSI.
The manufacturing process is adjusted such that the failure pressure is now normally distributed with mean 850 and standard deviation σ\sigmaσ.
Given that 98% of the adjusted valves fail between 835 PSI and 865 PSI, determine the value of σ \sigma\,σ to two decimal places.
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.