A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 50, and the sample standard deviation, s, is found to be 8.

(a) Construct a 98% confidence interval for u if the sample size n, is 15. How does decreasing the sample size affect the margin of error, E?

- Increases the margin of error

- Has no effect on the margin of error

- Decreases the margin of error

(b) Could the confidence interval have been constructed if the population had not been normally distributed? Why or Why not?