Normal distribution
Normal distribution turns up in 2 fields: statistics, metrology. Here is what it means to the people in each one.
Normal distribution in statistics
Symmetric bell-shaped distribution set by a mean and a standard deviation, the default model for measurement data.
The normal or Gaussian distribution puts about 68.3 percent of values within 1 standard deviation of the mean, 95.4 percent within 2 and 99.73 percent within 3. Control limits, capability indices and most significance tests assume it, either directly or through averages. Real process data are often skewed or bounded, such as particle counts or flatness that cannot go below zero, so a normal probability plot comes before any ppm prediction.
"Leakage is lognormal, not normal. Your Cpk of 1.5 is predicting ppm off a tail that doesn't exist."
Normal distribution in metrology
The bell-shaped distribution assumed for most certificate values and averaged readings, set by mean and standard deviation.
The symmetric bell-shaped probability distribution in which about 68.3 % of values fall within ±1 standard deviation, 95.45 % within ±2 and 99.73 % within ±3. It is assigned to an imported certificate uncertainty, to the mean of repeated readings and, through the central limit theorem, to the combined result when several comparable contributions are summed. To convert a normal expanded uncertainty to a standard uncertainty, divide by its stated coverage factor.
"Reference cert gives 0.02 percent at k equals 2, treat it as a normal distribution and divide by two."