confidence intervals. If convenient, use technology to construct the confidence intervals.

A random sample of $55$ home theater systems has a mean price of $$150\mathrm{.}00.$ Assume the population standard deviation is $$15\mathrm{.}60.$

Construct a $90\%$ confidence interval for the population mean.

The $90\%$ confidence interval is

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

Construct a $95\%$ confidence interval for the population mean.

The $95\%$ confidence interval is

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

Interpret the results. Choose the correct answer below.

wider than the $90\%.$

is wider than the $90\%.$

is narrower than the $90\%.$