z_star calculated via scipy can grow to infinty - Is this right? After years of "abstinence" I dabble back into statistics of population proportions and have some trouble making sense of critical values $z^\star$ for high confidence levels:
The critical value $z^\star$ is needed for the calculation of confidence intervals. I compute $z^\star$ from the confidence level cl with the Python module scipy via
cdf = 0.5+cl/2
z_star = scipy.stats.norm.ppf(cdf)

This z_star (i.e. $z^\star$) can grow to infinity, because
scipy.stats.norm.ppf(1)

outputs inf.
On the other hand, I'd say the confidence interval

$CI= \hat p \pm z^\star se(\hat p)$

can reasonably not exceed $[0\%,100\%]$.
How do these things fit together? 


*

*Is the scipy calculation an approximation with goes astray for confidence levels close to $100\%$? 

*Or is my idea that confidence intervals not exceed $[0\%,100\%]$ not general enough?

*Or is something with my cdf calculation wrong?


I would love some pointers here!
 A: At the end there you're using a normal approximation to a binomial proportion to obtain a confidence interval. The normal is continuous and has an infinite range while the binomial proportion is discrete and has a finite range; if you go sufficiently far into the tail of the normal you can go outside the possible range of the binomial parameter, $p$.
As the Wikipedia article Binomial proportion confidence interval puts it:      

A commonly used formula for a binomial confidence interval relies on approximating the distribution of error about a binomially-distributed observation, $\hat p$, with a normal distribution. This approximation is based on the central limit theorem and is unreliable when the sample size is small or the success probability is close to 0 or 1.

Here's an illustration of the problem:

If that occurs, you're outside the region of values for $p$ and $n$ where the approximation is good for those percentiles. Indeed you would usually want to stay a fair way from the 0/1 endpoints (a fairly large distance in terms standard errors of the proportion, though the absolute distance from the end might be small in a large sample)
