# How to interpolate for the normal distribution (or any other distribution)? [duplicate]

I have that X is normally distributed with mean 4 and variance 9 and I need to calculate the probability: Pr(X>9).

So far, I have Pr(X>9)=Pr(Z>5/3)=1-Pr(Z<5/3).

Now, the value for Pr(Z<5/3) is not in the tables. I remember back in school we used to have some sort of interpolation formula but I can't find it anywhere! Can anyone help?

Thanks!

This last paragraph is for amusement, and I would not recommend this approach unless I woke up tomorrow in the year 1900. If you are just really excited about interpolation, which some people are, you could use a linear approximation based on the two nearest values. In other words, if you have access to $p(Z < x_1)$ and $p(Z < x_2)$ for $x_1$ and $x_2$ on either side of $5/3$, you could use $$\frac{(5/3-x_1)p(Z < x_1) + (x_2-5/3)p(Z < x_2)}{x_2 - x_1}.$$