Title: 39_1 The Normal Distribution
Course: HELM Workbooks 2023-2024 > Section: HELM 39: The Normal Distribution

Mass-produced items should conform to a specification. Usually, a mean is aimed for but, due to random errors in the production process, a tolerance is set on deviations from the mean. For example, if we produce piston rings which have a target mean internal diameter of \(45\) \(\text{mm}\) then realistically we expect the diameter to deviate only slightly from this value. The deviations from the mean value are often modelled very well by the normal distribution. Suppose we decide that diameters in the range \(44.95\) \(\text{mm}\) to \(45.05\) \(\text{mm}\) are acceptable, then what proportion of the output is satisfactory?

In this Section we shall see how to use the normal distribution to answer questions like this.