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 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.