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.
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.