In the naive unsupervised anomaly detection algorithm, we go through each feature and calculate the probability of getting the value. Then, we multiply the probability for each feature to calculate the net probability.
But, in multiplication, we use the actual value on the normal curve: $$\frac{1}{\sigma \sqrt{2 \pi}} \exp{\left(-\frac{(x - \mu) ^ 2}{2\sigma^ 2}\right)}$$
Shouldn't we multiply by the area under the curve for getting such an extreme value i.e. the area under the curve for $(-\infty, -x) \cup (x, \infty)$
I can imagine a scenario where the $\sigma$ is high (the curve is highly spread out) and so even the probability of getting the mean is low.
How does this work then? Sorry if this is a stupid question, I am new to statistics.
Thanks!