A materials laboratory analyzes the composition and properties of high-precision components.
The concentration of xenon, CCC ppm, in a specific gas mixture is modeled by a normal distribution with a mean of 45.2 and a standard deviation of 1.2.
(a) (i) Find the probability that a randomly selected gas sample has a xenon concentration of exactly 45.2 ppm.
(a) (ii) Find the probability that a randomly selected gas sample has a xenon concentration less than 43.1 ppm.
The thickness of a protective gold coating, TTT μ\muμm, on a circuit component is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
(b) (i) Given that P(T<15.5)=0.95P(T < 15.5) = 0.95P(T<15.5)=0.95, show that
15.5−μ=1.645σ 15.5 - \mu = 1.645\sigma 15.5−μ=1.645σwhere the constant is given to three decimal places. Fully justify your answer.
(b) (ii) Given further that P(T<12.0)=0.20P(T < 12.0) = 0.20P(T<12.0)=0.20, find the values of μ\muμ and σ\sigmaσ.
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.