Each day a quality engineer selects a random sample of 50 po

Each day a quality engineer selects a random sample of 50 power supplies from the day\'s production, measures their output voltages, and computes a 90% confidence interval for the mean output voltage of all the power supplies manufactured that day. What is the probability that more than 16 of the confidence intervals constructed in the next 220 days will fail to cover the true mean? Hint: Use the normal approximation.

P(X > 16) =

Solution

Since 90% c.i is computed bu a process that covers the population mean 90% of the time. the success probability for each bernoulli trial is 1-0.9= 0.1
Y ~ B(200,0.1) ~ N ( 20,Sqrt(18))

P(X > 16) = (16-20)/4.2464
= -4/4.2464 = -0.942
= P ( Z >-0.942) From Standard Normal Table
= 0.8269