A scientific robotic probe collects soil samples from a lunar crater. The mass M M\,M grams of each sample is modeled as a normal distribution M∼N(μ,σ2)M \sim \mathrm{N}(\mu, \sigma^2)M∼N(μ,σ2). Based on an initial batch of data, a 90% confidence interval for μ \mu\,μ is calculated as (122.35,127.65)(122.35, 127.65)(122.35,127.65).
Determine a 99% confidence interval for μ\muμ.
The total yield of a specific mineral extract from a sample is given by the linear transformation Y=20MY = 20MY=20M. Using your answer from part (a), find a 99% confidence interval for the mean mineral yield μY \mu_Y\,μY of these samples.
If six independent random samples are taken and a 99% confidence interval for μ \mu\,μ is constructed for each, find the probability that at least five of these intervals will contain the true value of 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.