Question

How do you find the probability of `P(z < -2.58` or `z > 2.58)` using the standard normal distribution?

Answer 1

0.0098

Explanation:

Let's consult a z-table, such as this one. We only need one number: when z = -2.58 and we can do some math to get the final answer.
The table says that the P(`z < -2.58`) = .0049 or 0.49%.

We also know that the normal curve is symmetric, meaning that any area can be flipped (i.e. `P(z < z_0) = P(z > -z_0)` and visa versa). That means that `P(z < -2.58) = P(z > 2.58)`. Therefore, as originally asked,

`P(z <-2.58) + P(z > -2.58) = 2P(z < -2.58) = 0.0098`