Find the critical value Za/2 needed to construct a confidence interval with the given level Level 99.7%

1. Identify that the level of confidence is 99.7%.
2. Calculate the area in each tail:
- The confidence level of 99.7% means there's 0.3% in the tails combined.
- The area in one tail is \frac{0.3\%}{2} = 0.15\% .
3. Determine the z-score for the 99.85th percentile (since 0.15% in one tail means 99.85% in the bulk of the distribution under one tail).
4. Look up this value in the standard normal distribution table or using a calculator, the critical z-score is typically approximately 3.00 (for a standard normal distribution).
5. Conclude that z_{\frac{\alpha}{2}} = 3.00 for a 99.7% confidence interval.