# Creating a probability distribution from means and standard deviations

I want to look at an objective measure test to get the probability that a given patient falls under a category, in this case, functional level (K-Level)

+==============+==============+===============+===============+===============+===============+
|    AMPPRO    |   K-level    |     K0-K1     |      K2       |      K3       |      K4       |
+==============+==============+===============+===============+===============+===============+
| max score 47 | Mean score   | 25            | 34.65         | 40.5          | 44.67         |
+--------------+--------------+---------------+---------------+---------------+---------------+
|              | SD           | 7.37          | 6.49          | 3.9           | 1.75          |
+--------------+--------------+---------------+---------------+---------------+---------------+
|              | Range        | 17.63 - 32.37 | 28.16 - 41.14 | 36.60 - 44.40 | 42.92 - 46.42 |
+--------------+--------------+---------------+---------------+---------------+---------------+


Especially in the higher K-Levels as the SD goes down, the distinction between classifications becomes blurred. The test results are an integer score ranging from 0-47.

If I eyeball it, I can say that a patient who scores 43 is probably about 48.5% likely a K4, 48.5% likely a K3, 2% likely a K2, and 1% likely a K0-K1. I'm not good at formal statistics, so this would just give general the shape of the bar chart I would like to generate.

X axis is the bins you put your population into based on the score. Y axis is the probability, ranging from 0-1. You get two tiny bars for the bins "K0-K1" and "K2". Two big, roughly equal sized bars for "K3" and "K4".

Is there a way to do this... more mathematically? Is it possible to get a probability distribution with just Means and Standard deviations?