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.
225 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.