Yes !Would P(z<=1.62) be the same?
The difference in counting 1.62 or not comes with the fact that you're working on continuous or discrete variables.
If it's continuous, we rather work on intervals, that is to say an uncountable amount of values. Imagine you want the probability of X being between 0 & 1, where X can take any value between 0 & 1.
The probability of taking one value is 0.
If it's discrete, it means that the variable takes a countable amount of values, that is to say it takes specific values. So the probability that it takes one value can't be neglected.
A way to remember is that when working with discrete random variables, you work with a probability distribution, that is to say with the probability that the variable takes one value.
When working with continuous random variables, you work with a probability density function, that is to say that the probability will be representing an area. Does it matter including one point or not ?
I'm not sure whether it's clear or not