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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.