Construct a 95% Z-Interval or a 95% T-Interval About the Population

Multiple Choice

Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that
is approximately normal with no outliers.
-The heights of 20 - to 29 -year-old females are known to have a population standard deviation $\sigma = 2.7$ inches. A simple random sample of $n = 15$ females 20 to 29 years old results in the following data:
$\begin{array}{lllll}63.1 & 67.9 & 64.8 & 62.2 & 65.4 \\\hline 63.3 & 66.2 & 68.2 & 69.7 & 64.1 \\\hline 68.4 & 69.9 & 67.3 & 64.5 & 70.2\end{array}$

A) $( 64.98,67.72 )$ ; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.98$ and $67.72$ inches.
B) $( 64.85,67.85 )$ ; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $64.85$ and $67.85$ inches.
C) $( 65.12,67.58 )$ ; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.12$ and $67.58$ inches.
D) $( 65.20,67.50 )$ ; we are $95 \%$ confident that the mean height of 20 - to 29 -year-old females is between $65.20$ and $67.50$ inches.