The output from a process is normally distributed with a kno

The output from a process is normally distributed with a known standard deviation, but the mean is unknown. 24 different simple random samples, each with n=10 , are to be drawn from the process, and a 95% confidence interval for the mean is to be constructed for each sample. What is the probability that at least 21 of the confidence intervals will actually contain the population mean? Round your answer to the nearest percent.

Solution

p that a random mean is in this interval = 0.95

X no of intervals containing population mean is binomial with p = 0.95 and n = 24

P(X>=21)

= 0.9702