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.
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.