The concentration of a specific catalyst, C C\,C mg/L, in a chemical reaction follows a normal distribution where C∼N(μ,12.52)C \sim N(\mu, 12.5^2)C∼N(μ,12.52). Observations show that the catalyst concentration exceeds 145.6 mg/L in only 8.85% of trials.
Determine the value of the mean concentration μ\muμ.
Find the probability that the catalyst concentration in a randomly selected trial lies between the mean and 145.6 mg/L.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.