Am I reading Normal Distribution table correctly?

Question

Let's say I have a normal distribution with mean = 5.

Say $P(X>9) = .2$. Then does the following hold?

$1 - P(X<9) = .2$

$P(X<9) = .8$

$\frac{9-5}{\sigma} = .7881$

Or, am I reading this Normal Distribution table wrong?

Answer 1

You are reading the normal distribution table wrongly. The values inside the table are the probabilities.

$0.8$ is between $0.7995$ and $0.8023$, hence

$$0.84<\frac{9-5}{\sigma}<0.85.$$