Basic Technical Mathematics, 11th Edition

22.4 Normal Distributions

• Normal Distributions • Empirical Rule • z-Score • Standard Normal Distribution • Applications of Normal Distributions • Sampling Distribution of $\stackrel{\hspace{0.17em}¯\hspace{0.17em}}{\mathit{x}}$ • Standard Error

The distributions in the previous sections have been for a limited number of values. Let us now consider a very large population, such as the useable lifetime of all the AA batteries sold in the world in a year. It could have a large number of classes with many values within each class.

We would expect a histogram for this very large population to have its maximum frequency very near the mean and taper off to smaller frequencies on either side. It would probably be shaped something like the curve shown in Fig. 22.10.

Fig. 22.10

The smooth bell-shaped ...