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 (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.