**Definition 1**: A random variable *x* is **log-normally** distributed provided the natural log of *x*, ln *x*, is normally distributed. See Exponentials and Logs and Built-in Excel Functions for a description of the natural log.

**Observation**: As discussed in Transformations, sometimes it is useful to use a transformation of the population being studied. In particular, since the normal distribution has very desirable properties, transforming a random variable into a variable that is normally distributed by taking the natural log can be useful.

Note that the log-normal distribution is not symmetric, but is skewed to the right. If you have data that is skewed to the right that fits the log-normal distribution, you may be able to access various tests described elsewhere in this website that require data to be normally distributed.

**Excel Functions:** Excel provides the following two functions:

**LOGNORMDIST**(*x, μ, σ*) = NORMDIST(LN(*x*), *μ, σ,* TRUE)

**LOGINV**(*p, μ, σ*) is the inverse of LOGNORMDIST(*x, μ, σ*); i.e. LOGINV(*p, μ, σ*) = the value *x* such that LOGNORMDIST(*x, μ, σ*) = *p*

Excel 2010/2013 provide the following additional functions: **LOGNORM.DIST**(*x, μ, σ*, cum) where cum takes the values TRUE or FALSE and **LOGNORM.DIST**(*x, μ, σ*, cum) = NORM.DIST(LN(*x*), 0, 1, cum), and **LOGNORM.INV** which is equivalent to LOGINV.