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.
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.