Question

What is a probability distribution?

What is a continuous probability distribution?

Provide an example from business of the usefulness of a probability distribution and/or a continuous probability.

Answer 1

Probability Distribution: A probability distribution is a statistical function that identifies all the conceivable outcomes and odds that a random variable will have within a specific range. This range is determined by the lowest and highest potential values for that variable. For instance, if a company expects to bring in between $100,000 and $500,000 in monthly revenue, the graph will start with $100 at the low end and $500 at the high end. The graph for a typical probability distribution resembles a bell curve, where the least likely events fall closest to the extreme ends of the range and the most likely events occur closer to the midpoint of the extremes.

Continuous probability distribution: A probability distribution in which the random variable X can take on any value (is continuous). Because there are infinite values that X could assume, the probability of X taking on any one specific value is zero. The normal distribution is one example of a continuous distribution. The probability that X falls between two values (a and b) equals the integral (area under the curve) from a to b:

Example: A major application for probability distributions lies in anticipating future sales incomes. Companies of all sizes rely on sales forecasts to predict revenues, so the probability distribution of how many units the firm expects to sell in a given period can help it anticipate revenues for that period. The distribution also allows a company to see the worst and best possible outcomes and plan for both. The worst outcome could be 100 units sold in a month, while the best result could be 1,000 units sold in that month.