Theoretical percent out-of-spec formulas

To find theoretical % above spec:

Locate the value for Z_upper in a standard normal table.

To find theoretical % below spec:

Locate the value for Z_lower in a standard normal table.

Given:

• An X-bar value
  
  
• A sigma value and
  
  
• A set of specifications

And assuming:

• A normal distribution

In theory:

If the Z value from the standard normal table is multiplied by 100, then this process is expected to produce X% of its output outside specification.

Show me:
The standard normal table
The formulas for Target Z

Related topic:
The formula for actual percent out of spec