I was looking at these examples here:
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:-> The probability is 85.361%.
1b:-> 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?
If a distribution is genuinely continuous then it doesn't matter whether you include the endpoints, since the probability of taking a single value is zero.
In a real life example we would generally know the accuracy to which a measurement has been taken. For example, if the numbers have been rounded to the nearest whole number then between 65 and 80 would be from 64.5 to 80.5. So context is everything here.
Sorry that doesn't really clear up your question.
What software are you using? Maybe this will help:
1a) and 1b) look like Ti-83 commands.
I am getting the same answer as you for 1a) and 1b).
In mathematics, you don't understand things. You just get used to them.