The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of nnn observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (12.42,12.85)(12.42, 12.85)(12.42,12.85).
Show that the standard error used to find this confidence interval is 0.1100.1100.110 to 333 significant figures.
Using the same random sample,
find a 98%98\%98% confidence interval for μ\muμ. Give your answers to 333 decimal places.
The r%r\%r% confidence interval using the same random sample has a width of 0.500.500.50.
Calculate the value of rrr.
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.