Quantitative Analysis for Management, 13/e

2.7 The Normal Distribution

One of the most popular and useful continuous probability distributions is the normal distribution. The probability density function of this distribution is given by the rather complex formula

$$f\left(X\right)=\frac{1}{\sigma \sqrt{2\pi }}e\frac{{\mathrm{-}{\left(x-\mu \right)}^2}^{}}{{2{\sigma }^2}^{}}$$ (2-12)

The normal distribution affects a large number of processes in our lives (e.g., filling boxes of cereal with 32 ounces of corn flakes). Each normal distribution depends on the mean and standard deviation.

The normal distribution is specified completely when values for the mean, $\mu ,$ and the standard deviation, $\sigma ,$ are known. Figure 2.7 shows several different normal distributions with the same standard deviation and different means. As shown, differing values of $\mu$ will shift the average or center ...