A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume that gain is normally distributed with standard deviation $\backslash$sigma $=20.$

Find a $95\%$ CI for $\backslash$mu when n$=19$ and x $=1200$

Find a $95\%$ CI for $\backslash$mu when n$=32$ and x $=1200$

Find a $99\%$ CI for $\backslash$mu when n$=19$ and x $=1200$

Find a $99\%$ CI for $\backslash$mu when n$=32$ and x $=1200$

How does the length of the CIs computed above change with the changes in sample size and confidence level?

How large must n be if the length of the $95\%$ CI is to be $42?$