Take the following example. In the US, the average IQ is 100 points with a standard deviation of approx. 18 points. Find the following probability:
Find the probability that a randomly selected individual has an IQ of exactly 100 points.
Here is what I assume needs to be done, after which point we normalize and use tables.
a) $P(X = 100) \rightarrow P(99.5 < X < 100.5)$
Does this look right?
As a further question, would we need to do something similar every time the question asks to find the probability of choosing an individual with a score over or under but also equal to a certain value? For example, find the probability that a randomly selected individual has an IQ of 130 points or more. Would it be done like this??
$P(X \geq 130) \rightarrow P(X > 129.5)$
In other words, do we correct for continuity every time equality is involved?