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        "intro": "<p><span style=\"font-size: 14px;\">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\\)&nbsp;\\(\\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 <\/span><b style=\"font-size: 14px;\">normal distribution<\/b><span style=\"font-size: 14px;\">.&nbsp;<\/span>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?&nbsp;<\/p><p>In this Section we shall see how to use the normal distribution to answer questions like this.<\/p>",
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