A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03. Find the 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximate normal distribution

My final answer varies from the answer given in the textbook. I'd like for someone to go over my work and point out my error. Please double check my mean and standard deviation as well.

$\displaystyle \bar{x}=1.005556$

$\displaystyle \sigma=0.025442$

$\displaystyle \alpha=0.01$

$\displaystyle Z_{\frac{0.01}{2}}=2.575$Please double check this as well

$\displaystyle n=9$

$\displaystyle pr(1.005556-(2.575(\frac{0.025442}{\sqrt{9}}<\mu <1.005556+(2.575(\frac{0.025442}{\sqrt{9}})=0.99$

$\displaystyle pr(0.984482<\mu<1.026629)=0.99)$Is the final answer that I get. However, the book has

$\displaystyle 0.978<\mu<1.033$Can someone please tell me where my error is? Thanks.