1. Confidence interval. Need someone to check my answer

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.

$\bar{x}=1.005556$

$\sigma=0.025442$

$\alpha=0.01$

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

$n=9$

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

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

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

2. Nevermind. I'm an idiot. $\sigma$ is unknown so I need to use the t-distribution