If a normal distribution is used to model demand, what does its symmetry imply about deviations from the mean?

• A. Demand is always increasing
• B. Demand only takes two values
• C. Demand is always equal to the mean
• D. Demand fluctuates around the mean in a symmetric way

Answer: (D)

The main idea is that a normal distribution is symmetric about its mean, which means deviations from the mean come in equal positive and negative forms. In a normal model of demand, the value you observe is mu plus a random deviation, and the distribution of that deviation is centered at zero with the same likelihood for +d as for −d. So demand tends to hover around the mean, with fluctuations that are mirrored on either side—the farther you move from the mean, the less likely you are to see that value, and the left and right sides mirror each other. The result is a bell-shaped curve where most demand values cluster near the mean and symmetric tails extend in both directions. This doesn’t imply demand always increases, nor that it only takes two values, nor that it must equal the mean every time. It simply says deviations around the mean are equally likely in both directions.