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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
