The weights of mineral samples, W W\,W grams, collected by a deep-sea drone are normally distributed with an unknown mean μ \mu\,μ and a known variance σ2\sigma^2σ2. Based on a random sample of n n\,n observations of WWW, a 90% confidence interval for μ \mu\,μ was calculated as (45.32,46.18)(45.32, 46.18)(45.32,46.18).
Show that the standard error of the mean calculated from this sample is 0.261 to 3 significant figures.
Using the same random sample,
determine a 99% confidence interval for μ\muμ. Give your limits to 3 decimal places.
A different r% r\%\,r% confidence interval for μ \mu\,μ constructed from this same sample has a total width of 1.20 grams.
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.