Fun

Missing negative from the normal

A normal function isn’t so normal

The normal density function is:

$$ \large f(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp^{-\frac{(x - \mu)^2}{(2 \sigma^2)}} $$

It doesn’t make sense to calculate the probability for a single value in a continuous probability function, it is by definition zero, but you can calculate relative likelihoods (heights). dnorm simply gives the value of the function for a given x, not the area under the curve for that x (which is basically nothing for a single value). To find the density (height) for a single x value on the normal distribution, use dnorm() in the following way (here each x value is treated as separate and vectorized over),