This distribution is also called skewed. If a set of numbers is log-normally distributed, 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 relationship 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

, and a mean

.

© John Wiley & Sons, Inc.

FIGURE 24-3: The log-normal distribution.

The Binomial Distribution

The binomial distribution helps you estimate the probability of getting x successes out of N

independent tries when the probability of success on one try is p. (See Chapter 3 for an introduction to

probability.) A common example of the binomial distribution is the probability of getting x heads out of

N flips of a coin. If the coin is fair, p = 0.5, but if it is lopsided, p could be greater than or less than 0.5

(such as p = 0.7). Figure 24-4 shows the frequency distributions of three binomial distributions, all

having

but having different N values.

© John Wiley & Sons, Inc.

FIGURE 24-4: The binomial distribution.

The formula for the probability of getting x successes in N tries when the probability of success on one

try is p is

.