Using two different confidence levels, a researcher constructs two contidence intervais for a population mean based on one sample taken from a normal population with known population variance ${}^2=1024.$ The standard error of the mean is $5\mathrm{.}191.$

The confidence intervals are:

Interval $1$:

Interval $2$:

Determine the following:

a$)$ The sample mean $(1$ decimal place$)$:

$\stackrel{}{x}=$

b$)$ The margin of error, $ME(2$ decimal places$)$:

$ME$ for Interval $1=$

$ME$ for Interval $2=$

c$)$ The sample size $($to the nearest integer$)$:

$n=$

At what confidence level was each confidence interval constructed? Choose the closest.

a$)$ What is the confidence level used in Interval $1?$