The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of 16 observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (40.04,43.96)(40.04, 43.96)(40.04,43.96).
Find the mean of the sample.
Show that the standard deviation σ\sigmaσ is 4.
The a%a \%a% confidence interval using the 16 observations has a width of 3.3.
Calculate the value of aaa.
Find the smallest sample size, of observations from XXX, that would be required to obtain a 95%95\%95% confidence interval for μ\muμ of width at most 2.5.
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.