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.
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.