The concentration of a rare-earth element in a soil sample, denoted by the random variable CCC, follows a normal distribution with an unknown mean μ\muμ and a known variance σ2\sigma^2σ2. A geologist collects a random sample of nnn measurements of CCC, which results in a 90%90\%90% confidence interval for μ\muμ of (45.82,47.18)(45.82, 47.18)(45.82,47.18).
Show that the standard error of the mean calculated from this sample is 0.4130.4130.413 to 333 significant figures.
Using the same random sample,
find a 99%99\%99% confidence interval for μ\muμ. Give your limits to 333 decimal places.
The r%r\%r% confidence interval calculated from the same sample data has a total width of 1.801.801.80.
Calculate the value of rrr, giving your answer to 111 decimal place.
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.