You are given the sample mean and the population standard deviation. Use this information to construct the $90\%$ and $95\%$ confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of $59$ dates, the mean record high daily temperature in a certain city has a mean of $86\mathrm{.}31F.$ Assume the population standard deviation is $14\mathrm{.}78F.$

The $90\%$ confidence interval is $,|||$

$($Round to two decimal places as needed.$)$

The $95\%$ confidence interval is $(,|).$

$($Round to two decimal places as needed.$)$

Which interval is wider? Choose the correct answer below.

The $95\%$ confidence interval

The $90\%$ confidence interval

Interpret the results.

A$.$ You can be $90\%$ confident that the population mean record high temperature is between the bounds of $90\%$ confidence interval, and $95\%$ confident for the $95\%$ interval.

B$.$ You can be certain that the mean record high temperature was within the $90\%$ confidence interval for approximately $53$ of the $59$ days, and was within the $95\%$ confidence interval for approximately $56$ of the $59$ days.

C$.$ You can be certain that the population mean record high temperature is either between the lower bounds of the $90\%$ and $95\%$ confidence intervals or the upper bounds of the $90\%$ and $95\%$ confidence intervals.

D$.$ You can be $90\%$ confident that the population mean record high temperature is outside the bounds of the $90\%$ confidence interval, and $95\%$ confident for the $95\%$ interval.