Question

compute the critical value z a/2 that corresponds to a 93% level of confidence.

Answer 1

You want to find \(Z_{\alpha/2}\) such that
\[P(Z>Z_{\alpha/2})=\frac{1-0.93}{2}=0.035\]
assuming \(Z_{\alpha/2}>0\).

Graphically, you want to find the dotted lines that separate the population into chunks of \(0.93\) and \(\dfrac{1-0.93}{2}\):

This is a matter of referring to a table of \(z\) values. The probability above is a right-tail probability, so you have to make sure you use the correctly-tailed table of values.

Here I'll link you to a left-tail table:
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

In this case, we have the equivalence
\[P(Z>Z_{\alpha/2})=P(Z<-Z_{\alpha/2})=0.035\]
We find that \(-Z_{\alpha/2}\) must be about \(-2.70\), so \(Z_{\alpha/2}=2.70\).