Using the Z-Table in Reverse: from the regions to the Z-values

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In a "forward direction" use of the Z-Table, you'll often

  1. Start with a normal distribution with mean and standard deviation
  2. Transform a value to a standard normal, to a standard , via
  3. Find an area value from the Z-Table, corresponding to .
Normal backwards.png

In the "backward direction", you do these three steps in reverse:

  1. Starting with an area, you
  2. Find the corresponding of the area, considered as
  3. Transform the Z-values from the standard normal to the original normal values, via the transformation