Which description correctly describes a log-normal distribution?

Which description correctly describes a log-normal distribution?

• A. A distribution that has a central location to the left.
• B. A symmetric bell-shaped distribution.
• C. A distribution across a finite range.
• D. A distribution that has a central location to the left and is positively skewed (long tail to the right).

Answer: (D)

Think of a log-normal as what you get when you exponentiate a normal distribution. That makes it defined only for positive values, and it is not symmetric. Most of the data sit near smaller values, but there is a long tail extending to larger values. This combination—bulk on the left with a long right tail—is exactly what is described here. The log-normal isn’t a symmetric bell curve, and it isn’t limited to a finite range, so descriptions that imply symmetry or a bounded interval don’t fit. The emphasis on a left-centered peak with a long right tail captures the essential shape of a log-normal distribution, which often arises when a variable is the product of many positive factors or when you model things that can’t go below zero but can grow large.

Think of a log-normal as what you get when you exponentiate a normal distribution. That makes it defined only for positive values, and it is not symmetric. Most of the data sit near smaller values, but there is a long tail extending to larger values. This combination—bulk on the left with a long right tail—is exactly what is described here. The log-normal isn’t a symmetric bell curve, and it isn’t limited to a finite range, so descriptions that imply symmetry or a bounded interval don’t fit. The emphasis on a left-centered peak with a long right tail captures the essential shape of a log-normal distribution, which often arises when a variable is the product of many positive factors or when you model things that can’t go below zero but can grow large.