# A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 111​, and the sample standard​ deviation, s, is found to be 11.   ​(a) Construct a 95​% confidence interval about μ if the sample​ size, n, is 21. ​(b) Construct a 95​% confidence interval about μ if the sample​ size, n, is 12. ​(c) Construct a 90​% confidence interval about μ if the sample​ size, n, is 21.

Question
A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 111​,
and the sample standard​ deviation, s, is found to be 11.

​(a) Construct a 95​% confidence interval about μ if the sample​ size, n, is 21.
​(b) Construct a 95​% confidence interval about μ if the sample​ size, n, is 12.
​(c) Construct a 90​% confidence interval about μ if the sample​ size, n, is 21.
​(d) Should the confidence intervals in parts​ (a)-(c) have been computed if the population had not been normally​ distributed?

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Math
Statistics