Question

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

Answer 1

We looking for the value z that provides a confidence interval with a level of 99.7%, In order to find the value of Za/2 calculate

$100-99.7=0.3\Rightarrow\frac{0.3}{2}=0.15\Rightarrow99.7+0.15=99.85\%$

Then, look in the Z table for the z value

$P(Z\leq z)=0.9985\Rightarrow z=2.9677$

Therefore, the answer is z=2.9677.