A geochemist analyzes the mass of rare lithium crystals found in a specific geological formation. The masses are known to be normally distributed with a mean μ \mu\,μ and a standard deviation of 1.2 mg. A random sample of 8 crystals is extracted, and their masses, in mg, are recorded as follows:
45.2,47.1,44.8,46.5,43.9,45.8,46.2,44.5 45.2, 47.1, 44.8, 46.5, 43.9, 45.8, 46.2, 44.5 45.2,47.1,44.8,46.5,43.9,45.8,46.2,44.5Calculate a 98% confidence interval for μ\muμ, giving your limits correct to two decimal places.
The geochemist later decides to collect 30 independent random samples, each consisting of 8 crystals. For each of these 30 samples, a 98% confidence interval for μ \mu\,μ is constructed.
Determine the probability that exactly one of these 30 intervals will not contain the true population mean 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.