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In: Statistics and Probability

A simple random sample of size n is drawn from a population that is normally distributed....

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x bar​,is found to be 114​, and the sample standard​ deviation, s, is found to be 10.

​(a) Construct an 80​% confidence interval about muμ if the sample​ size, n, is 22. Make sure to record the lower bound and upper bound.

​(b) Construct an 80​% confidence interval about muμ if the sample​ size, n, is 13. Make sure to record the lower bound and upper bound.

​(c) Construct a 70​% confidence interval about muμ if the sample​ size, n, is 22. Make sure to record the lower bound and upper bound.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

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