Unlike the RAND() function that generates real numbers only between 0 and 1, the Analysis ToolPak's Random Number Generation tool can produce numbers in any range and can generate different distributions, depending on the application. Table 12.2 summarizes the seven available distribution types.

Table 12.2. The Distributions Available with the Random Number Generation Tool

Distribution

Description

Uniform

Generates numbers with equal probability from the range of values you provide. Using the range 0 to 1 produces the same distribution as the RAND() function.

Normal

Produces numbers in a bell curve (normal) distribution based on the mean and standard deviation you enter. This is good for generating samples of things such as test scores and population heights.

Bernoulli

Generates a random series of 1s and 0s based on the probability of success on a single trial. A common example of a Bernoulli distribution is a coin toss (in which the probability of success is 50%; in this case, as in all Bernoulli distributions, you would have to assign either heads or tails to be 1 or 0).

Binomial

Generates random numbers characterized by the probability of success over a number of trials. For example, you could use this type of distribution to model the number of responses received for a direct-mail campaign. The probability of success would be the average (or projected) response rate, and the number of trials would be the number of mailings in the campaign.

Poisson

Generates random numbers based on the probability of a designated number of events occurring in a time frame. The distribution is governed by a value, Lambda, that represents the mean number of events known to occur over the time frame.

Patterned

Generates random numbers according to a pattern that's characterized by a lower and upper bound, a step value, and a repetition rate for each number and the entire sequence.

Discrete

Generates random numbers from a series of values and probabilities for these values (in which the sum of the probabilities equals 1). You could use this distribution to simulate the rolling of dice (where the values would be 1 through 6, each with a probability of 1/6; see the following example).