# Normal distribution for x>3,5

## Main Question or Discussion Point

Hi,
I'd like to know the value that $$\Phi(x)$$ of a normal distribution is approximated when x> 3,5.
I assume it is 1, since the value for x=3,49 is 0,9998...
But I got some answers at the university that it might be 0,5

Thanks

## Answers and Replies

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There is no finite value of for which it is 1: that is, if you calculate precisely, it will always be the case that $\Phi(x) < 1$ for a finite number $x$. For example, $\Phi(4) \approx 0.9999683$ and $\Phi(5) \approx 0.9999997$ (calculation from R software). However, just like my two examples, the values essentially get so close to 1 that the difference is, for almost all situations, immaterial.
For your second comment ("But I got some answers at the university that it might be 0,5") - if you mean 0.5, that is definitely false: the only value that gives $\Phi(x) = 0.5$ is
$x = 0$.