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

1 Answer
Jake M.
Mar 18, 2018

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 #

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