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 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.