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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.