# Inverse of the Standard Normal Cumulative Distribution Calculation

#### andreja

##### New Member
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?

Cheers!

#### andreja

##### New Member
Hi TheEcologist,

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

Cheers!

#### andreja

##### New Member
Hi TheEcologist,

Sorry, thats issue is solved.

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

Where:
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.

Cheers!

#### Dason

How exactly did you solve the problem with the normal distribution?

#### andreja

##### New Member
Hi Dason,

I have got it the manual formula by hand. Thanks

#### andreja

##### New Member
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

Cheers!

#### Dragan

##### 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.