Normal Distribution P(Z= 1.75)

Question

My textbook does not have any solution for this type of problem but it asks it. I cant find anyway to do it even with google...... I do not understand, my professor gave the solution and it is 0. I have no idea how that is

Answer 1

For [continuous] random variables $Z$ with a density $f$, we always have $P(Z=z)=0$.

One way to see this is to note that the probability of any interval $(a,b)$ is $P(a<Z<b) = \int_a^b f(x) \mathop{dx}$. If you imagine shrinking down this interval to a point $z$, then in the limit you will get $P(Z=z)=0$.