I was looking at these examples here:
Example 1: Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find:
a) the probability that a value is between 65 and 80, inclusive.
b) the probability that a value is less than 62.
1a: $normalcdf(65, 80, 70, 4.5)$ -> The probability is 85.361%.
1b: $normalcdf(-E^{99}, 62, 70, 4.5)$ -> The probability is 3.772%.
I'm kind of confused if nornamlcdf() is inclusive or exclusive. It seems to be inclusive in 1a. because the upperbound and lowerbound include 65 and 80. In 1b. it asks for values less than 62, so if the upper and lower bound are not inclusive than why is the upperbound 62 instead of 61?
Let $X$ denote any random variable with a density, such as any nondegenerate normal random variable. Then, for every $x$, $$ P(X\leqslant x)=P(X\lt x), $$ and, for every $x$ and $y$, $$ P(x\leqslant X\leqslant y)=P(x\leqslant X\lt y)=P(x\lt X\leqslant y)=P(x\lt X\lt y). $$