what is the official/academic name of an area under the right-tailed standard normal curve and how to compute the quantity?

Question

I am familiar with the CDF of the standard normal distribution.

here is the formula.

$$ \varPhi(x) = \int_{-\infty}^{x} \frac{e^{-u^{2}/2}} {\sqrt{2\pi}} du $$

there is an quantify which seems to be derived from the CDF of the standard normal distribution.

this post call it Z-Table (right) or right tail z table. this post call it areas under the one-tailed standard normal curve.

what is its official/academic name in statistic or probability theory?

how to derive a formula to compute this quantity?

Answer 1

the formula is

$$ \varPhi(x) - 0.5 = \left(\int_{-\infty}^{x} \frac{e^{-u^{2}/2}} {\sqrt{2\pi}} du\right) - 0.5 $$

I want this name, too.

Answer 2

based on @brennn

you could compute this quantity in R.

> pnorm(1.45) - 0.5
[1] 0.4264707