Given the distribution
$$\frac{1}{1.01\sqrt{2\pi}}e^{-\dfrac{1}{2}\left(\dfrac{x - 19.47}{1.01}\right)^2},$$
how do I find the probability involving the normal distribution for $P(X \le 16.50)$?

I want to find it using integration and I know there's something to do with the Maclurin or Taylor series.