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2.4.12 Calculate probabilities from a Normal distribution (A-level only)

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

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Question 49

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:

a.

the value of μ\muμ, giving your answer to two decimal places.

[4]
b.

the percentage of valves that are expected to withstand a pressure of more than 875 PSI.

[3]
c.

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.

[5]
Markscheme

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions

  1. A Level
  2. /Maths
  3. /2.4.12 Calculate probabilities from a Normal distribution (A-level only)

149 exam-style questions on OCR (MEI) A Level Maths 2.4.12 Calculate probabilities from a Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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