Answer
$295.2\lt\mu\lt397.3$
Work Step by Step
1. The mean value of the data set can be found as $\bar X=346.25$
2. At 92% confidence, use table E or a calculator, the critical z-value can be
found as $z_{\alpha/2}=1.75$
3. Given $\sigma=165.1, n=32$, the error of estimation can be found as
$E=1.75\times\frac{165.1}{\sqrt {32}}=51.07$
4. the interval of the mean can be found as
$\bar X−E\lt\mu\lt\bar X+E$ which gives $295.2\lt\mu\lt397.3$
