title: Python: calculate probability for each value in a column to be valid
body: <p>I have a pandas dataframe like this:</p>
  
  <pre><code>+-----+----------+
  | No  | quantity |
  +-----+----------+
  |   1 |    100.0 |
  |   2 |    102.3 |
  |   3 |    301.2 |
  |   4 |    100.6 |
  |   5 |    120.9 |
  | ... |      ... |
  +-----+----------+
  </code></pre>
  
  <p>How can I calculate the probability for each value that it does fit into the dataset (in dataframe above all do except of No.3). The idea is using the standardized normal distribution and calculate the probability, that a value (or more extreme one) would occur. In this case, probability that No.3 occurs is almost zero because it is far from all other values. </p>
  
  <p>I know how to do this on paper for each value:</p>
  
  <ol>
  <li><p>calculating z-score </p></li>
  <li><p>find the corresponding value in the standard normal probabilities-table</p></li>
  <li><p>if value is below average of the distribution, the probability is 1-probability</p></li>
  </ol>
  
  <p>so desired output is something like this:</p>
  
  <pre><code>+-----+----------+--------+
  | No  | quantity |  prob  |
  +-----+----------+--------+
  |   1 |    100.0 | 99,85% |
  |   2 |    102.3 | 99,81% |
  |   3 |    301.2 | 00,00% |
  |   4 |    100.6 | 99,90% |
  |   5 |    120.9 | 74,30% |
  | ... |      ... | ...    |
  +-----+----------+--------+
  </code></pre>
  
  <p>How can I realize that in python?</p>
  
  <p>Thank you :)</p>