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.
