Answer
2.575.
Work Step by Step
$\alpha=1-confidence \ level=1-99$%$=1-0.99=0.01.$
Hence $1-\frac{\alpha}{2}=1-0.005=0.995.$
$z_{\frac{\alpha}{2}}$ is the z score belonging to the probability of $1-\frac{\alpha}{2}=0.995$, which is 2.575.
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