Many of the business outcomes that managers care about are counts—the number of defectives in a batch, the number of complaints resolved in a day, and the number of respondents who recognize my brand, to name just a few. With just a few plausible assumptions, such variables will follow one of three standard probability distributions. The point of knowing the distribution is that you can predict the likely range of the business variable and even say how likely it is to be larger or smaller than some level of interest. For instance, you could state the probability of there being more than 12 defectives in a shipment of 500.
Suppose that you survey 500 customers on whether or not they recognize your brand. Suppose also that on the basis of historical norms you expect 35% or 175 to recognize your brand. But you have been spending more money than usual on advertising. How many more than 175 would convince you that the extra money had been worth the expense? You would not be convinced with 176 brand recognitions. It would need to be higher than this to really convince you. You would need to know what an improbably high value is.
This example involves counting up how many times something happens out of a fixed number of opportunities (called trials). This kind of count is described by the binomial distribution.
Suppose that you have to supply an order for five very expensive computer chips. ...