A Random Sample of 80 Observations Produced a Mean $\bar { x } = 35.4$

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $= 3.1$ .
a. Find a $90 \%$ confidence interval for the population mean $\mu$ .
b. Find a $95 \%$ confidence interval for $\mu$ .
c. Find a $99 \%$ confidence interval for $\mu$ .
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?