An agricultural scientist is measuring the heights of a specific variety of wheat plants, H H\,H cm, such that H∼N(μ,σ2)H \sim \operatorname{N}(\mu, \sigma^2)H∼N(μ,σ2).
A random sample of these plants is taken, and a 98% confidence interval for μ \mu\,μ is calculated as (78.14,82.26)(78.14, 82.26)(78.14,82.26).
Find, to 2 decimal places, the standard error of the mean.
Hence, or otherwise, calculate a 95% confidence interval for μ \mu\,μ based on the same sample of wheat plants.
Using five different random samples, five 95% confidence intervals for μ \mu\,μ are to be constructed.
Calculate the probability that at least 4 of these intervals will contain μ\muμ.
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.