Answer
$\mu$ is between 28.4 and 38.8.
Work Step by Step
The mean can be counted by summing all the data and dividing it by the number of data: $\frac{32+32+...+25}{15}=33.6.$
Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(32-33.6)^2+...+(25-33.6)^2}{14}}=7.67.$
$\alpha=1-0.98=0.02.$ $\sigma$ is 7.67, hence we use the z-distribution with $df=sample \ size-1=15-1=14$ in the table. $z_{\alpha/2}=z_{0.01}=2.33.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.33\cdot\frac{7.67}{\sqrt{15}}=5.2.$ Hence the confidence interval:$\mu$ is between 33.6-5.2=28.4 and 33.6+5.2=38.8.
