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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.