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 15 of the confidence intervals constructed in the next 200 days will fail to cover the true mean?
What will be an ideal response?
Let X be the number of 90% confidence intervals that fail to cover the true mean.
Then X ~ Bin(200,0.10), so X is approximately normal with mean 
= 200(0.10) = 20 and standard deviation
To find P(X > 15), use the continuity correction and find the z-score of 15.5.
The z-score of 15.5 is (15.5 ? 20)/4.242641 =?1.06.
The area to the right of z = ?1.06 is 1 ? 0.1446 = 0.8554.
P(X > 15) = 0.8554.
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