Fitting a Normal Curve 🧬

Overview: Given a frequency distribution, we want to find the theoretical frequencies assuming the data comes from a Normal Population.

Method of Ordinates vs Method of Areas

• Ordinates Method: Matches the height Y.
• Area Method (Preferred): Matches the probability areas.

Steps (Area Method) 🚶

1. Calculate Parameters: Find Mean (X̄) and Standard Deviation (σ) from the observed data.
2. Standardize Class Limits: Convert the lower limit (X1) and upper limit (X2) of each class interval into Z-scores.
   • Z1 = (X1 - Mean) / SD
   • Z2 = (X2 - Mean) / SD
3. Find Areas: Use the Standard Normal Table to find the area corresponding to Z1 and Z2.
4. Find Probabilities: Calculate area for the interval (Subtract or Add areas based on sign of Z).
5. Expected Frequency: Frequency = Total N * Area.

Application 🏭

Used to check if a process is under control or if the products follow standard norms.

• Example: Fitting a curve to weights of 1000 packets of sugar.
  • Find Mean (e.g., 995g) and SD (e.g., 5g).
  • Calculate expected packets in range 990-1000g.

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