A biologist is studying the weight of a rare species of caterpillar. The weights are known to be normally distributed with mean μ\muμ mg and standard deviation 1.2 mg1.2\text{ mg}1.2 mg. A random sample of 888 caterpillars is weighed, and their masses, in mg, are recorded as follows:
42.5,41.2,44.8,43.6,40.5,42.1,45.3,41.6 42.5, 41.2, 44.8, 43.6, 40.5, 42.1, 45.3, 41.6 42.5,41.2,44.8,43.6,40.5,42.1,45.3,41.6Calculate a 98%98\%98% confidence interval for μ\muμ, giving your limits correct to two decimal places.
The biologist plans to collect 303030 further independent random samples, each consisting of 888 caterpillars. For each sample, a 98%98\%98% confidence interval for μ\muμ will be constructed.
Determine the probability that exactly 333 of these 303030 intervals will not contain 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.