Inverse of the Standard Normal Cumulative Distribution Calculation

Hi Everyone,

I'm trying to verify the calculation for the Inverse Cumulative Standard Normal Distribution Function represented by the Excel function NORMSINV(p).

For instance: The Excel function =NORMSINV(0.9626) returns 1.78.

Anyone could show me a manual calculation for this?

Thanks in advance

Hi TheEcologist,

I know this page but I cannot translate it. Would you like show me step by step to calculate it?!

I appreciate your helps in advance.

Hi TheEcologist,

Sorry, thats issue is solved.

I have new issue about two-tailed inverse of the student`s t-distribution. I am trying to use calculation for two-tailed inverse of the student`s t-distribution function presented by Excel functions like =TINV(probability, deg_freedom).

alpha (a)= 0.05
degree of freedom (df)= 1221
p (two-tailed)= 0.0000408831

Next, just do calculate for two-tailed INVERSE of the student`s t-distribution using Excel formula as below;

=TINV(probability, deg_freedom)
=TINV(0.0000408831, 1221)
= 4.117456798

Resulted: 4.117456798

Could you show me a manual calculation step by step for this.

Appreciate your helps.

Dear All,

The manual formula mean that how to calculate that value by hand for TINV(0.0000408831, 1221) and the resulted is 4.0891672

Appreciate your help in advance.



Super Moderator
Note that you can also use the following Taylor series-based expansion for the standard normal cdf as:

\(\Phi \left ( Z \right )=\frac{1}{2}+\phi \left ( Z \right )\left \{ Z+\frac{z^{3}}{3}+\frac{z^{5}}{3\times 5}+ \frac{z^{7}}{3\times 5\times 7}+\cdot \cdot \cdot \cdot \cdot \right \} \)

where little phi is the height of the standard normal pdf at Z. It's excellent for Monte Carlo or Simulation studies.


Ambassador to the humans
Hi Dason,

I have got it the manual formula by hand. Thanks
There is no closed form expression that gives you the thing you're looking for exactly. Which is why I asked how you solved it because I want to know which method you were using.