# Math Help - w/percentile input calculate number of STDs from 0 ...

1. ## w/percentile input calculate number of STDs from 0 ...

I need to recreate an old function. Before I came into the picture my friend had a hard drive crash and lost the original documentation and source code, no backups, OH MY!

We only have a short description left:

Function: NormalCDF[Percentile], returns the number of standard deviations "Percentile" is from 0 using the standard normal distribution with mean 0 and standard deviation 1.

The name of the function seems misleading to me, At first I thought it referred to the cumulative distribution function (CDF) of a normal distribution. But that doesn't seem to make sense from the description.

I'll use Mathematica to implement the new version of this. It has an internal function to generate a Normal distribution with mean 0 and standard deviation 1:

NormalDistribution[0, 1]

Maybe the cumulative distribution function has some equivalence to "the number of standard deviations "Percentile" is from 0..."

I can also plot a CDF of the normal distribution like this:

Plot[CDF[NormalDistribution[0, 1], x], {x, -4, 4}]

but I don't feel like this gets me on the right track.

Regardless of the name of the function I need to do this:

Given a percentile input, calculate the number of standard deviations from 0 using a normal distribution

Any ideas?

2. I take it you want something like this

In Out
100% 3.9
95%1.645
60%0.253
50%0
30%-0.525

If so you need the inverse of the CDF of the standard normal distribution function.

Maybe Mathematica has this built in?

If not you can get tables of these values and use a table look up and interpolation. I believe there are polynomial approximations too but I really should be doing my own work so I'll leave the rest to you.

3. Originally Posted by a^2
I need to recreate an old function. Before I came into the picture my friend had a hard drive crash and lost the original documentation and source code, no backups, OH MY!

We only have a short description left:

Function: NormalCDF[Percentile], returns the number of standard deviations "Percentile" is from 0 using the standard normal distribution with mean 0 and standard deviation 1.

The name of the function seems misleading to me, At first I thought it referred to the cumulative distribution function (CDF) of a normal distribution. But that doesn't seem to make sense from the description.

I'll use Mathematica to implement the new version of this. It has an internal function to generate a Normal distribution with mean 0 and standard deviation 1:

NormalDistribution[0, 1]

Maybe the cumulative distribution function has some equivalence to "the number of standard deviations "Percentile" is from 0..."

I can also plot a CDF of the normal distribution like this:

Plot[CDF[NormalDistribution[0, 1], x], {x, -4, 4}]

but I don't feel like this gets me on the right track.

Regardless of the name of the function I need to do this:

Given a percentile input, calculate the number of standard deviations from 0 using a normal distribution

Any ideas?

Sounds like what you need is the inverse of the cumulative normal distribution.

Then

$z=Q^{-1}(x/100)$

where $x$ is a percentile say $x=75$ then the $z$ score corresponding tothe $75$ percentile is:

$z=Q^{-1}(0.75)$

RonL