A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 107, and the sample standard deviation, s, is found to be

10.

(a) Construct a 95% confidence interval about if the sample size, n, is 27.

(b) Construct a 95% confidence interval about if the sample size, n, is 20.

(c) Construct an 80% confidence interval about if the sample size, n, is 27.

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