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.
