How can I find a Z score from a p-value? How can I find a Z score from a p-value? I know how to look up the p-value from a Z score using a Normal distribution table, but I don't know how to calculate it.
For example, a question says the alpha equals 5 percent. From this, I see in my handout that the Z score is calculated to be 1.65.  How do I determine this?
Thank you.
 A: Typically the tables for $p$-values for the $Z$ distribution are arranged with values of $Z$ defining the row and column headers, and the body of the table consists of $p$-values.
If you are given a $Z$ value, you go to the corresponding row and column to look in the table. However, you can do the reverse of this, right? Given $p$ (or $\alpha$), you can find this value in the table and then look at the row and column headers to get $Z$.
Ta da!
A: Actually, $z_{.95}=1.6\underline{\mathbf{4}}$; your handout is LIES! (I'm being facetiously hyperbolic because the author seems to have rounded up somewhat improperly. It's not really a big deal.)
In r, the qnorm function converts probabilities (akin to distribution quantiles) to z-scores. Thus:
> qnorm(.95)
[1] 1.644854

The documation for qnorm lists the following reference for the algorithm, in case you want it. If you prefer not to use R, John Walker's calculator works through JavaScript-enabled web browsers. He also offers some equations that could be rearranged to do this by hand. You may also wish to check "How to deal with Z-score greater than 3?"

Reference
Wichura, M. J. (1988) Algorithm AS 241: The percentage points of the normal distribution. Applied Statistics, 37, 477–484.
