CHAPTER 24 Ten Distributions Worth Knowing 353

The Normal Distribution

The most popular and widely-used distribution is the normal distribution (also

called the Gaussian distribution and the probability bell curve). It describes variables

whose fluctuations are the combined result of many independent causes.

Figure 24-2 shows the shape of the normal distribution for various values of the

mean and standard deviation. Many other distributions (binomial, Poisson,

Student t, chi-square, Fisher F) become nearly normal-shaped for large samples.

The Microsoft Excel statement NORMSINV RAND

(

()) generates a normally

distributed random number, with mean 0 and SD 1.

The Log-Normal Distribution

This distribution is also called skewed. If a set of numbers is log-normally distrib-

uted, then the logarithms of those numbers will be normally distributed (see the

preceding section “The normal distribution”). Laboratory values such as enzyme

and antibody concentrations are often log-normally distributed. Hospital lengths

of stay, charges, and costs are also approximately log-normal.

You should suspect log-normality if the standard deviation of a set of numbers is

so big it’s in the ballpark of the size of the mean. Figure 24-3 shows the relation-

ship between the normal and log-normal distributions.

If a set of log-normal numbers has a mean A and standard deviation D, then the

natural logarithms of those numbers will have a standard deviation

s

Log

D

A

1

2

/

, and a mean m

Log A

s

2

2

/

.

FIGURE 24-2:

The normal

distribution at

various means

and standard

deviations.

© John Wiley & Sons, Inc.