A geologist is studying the depth, DDD metres, of carbon sequestration in a specific geological formation. The depth is modelled by a normal distribution with mean μ=1250\mu = 1250μ=1250 m and standard deviation σ=80\sigma = 80σ=80 m.
Find an estimate for the proportion of sequestration sites with a depth of less than 110011001100 m.
The research project involves two stages. Every site in the survey is measured in the first stage, and the deepest 12%12\%12% of sites are categorised as 'High Priority' for a more detailed second stage of testing.
Find an estimate for the minimum depth a site must have in the first stage to be categorised as High Priority. Give your answer to 4 significant figures.
Determine the median depth of the High Priority sites based on the first stage measurements.
The measurement in the second stage is independent of the first and follows the same normal distribution. A site receives 'Gold Status' if it is categorised as High Priority and its second stage measurement exceeds 140014001400 m.
A site is selected at random from the survey.
Find the probability that this site receives Gold Status.
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.