Prediction Interval
Prediction Interval
\[PI=\bar{x}\pm z\sigma\sqrt{1+\frac{1}{n}}\]
Variables
PI1 = lower prediction limit
PI2 = upper prediction limit
xb = sample mean
z = critical z value
sigma = population standard deviation
n = sample size
Description
What is this formula?
This formula calculates the prediction interval for a future observation assuming a normally distributed population with known standard deviation.
When to use it
Use this formula when estimating the range where a future individual observation is expected to fall with a specified confidence level.
Example
If a manufacturing process has a known average and variability, the formula can estimate the likely range of the next measured product dimension.
Applications
Quality assurance, forecasting, industrial process control, engineering measurements, laboratory analysis, and statistical prediction.
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