Find the following probabilities for a standard normal distribution $P(|Z| > 2.05)$

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I have

• $P(|Z| > 2.05)$
• $P(-2.05 < Z < 2.05)$
• $P(Z < 2.05) - P(Z < -2.05)$
• $0.9798 - 0.0202$

and got my answer to be $0.9596$ but it seems off. I do not know where I missed a step. Any help would be much appreciated.

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1 Answer

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You made an error in step 2:

$P(|Z|>2.05) = P(Z > 2.05) + P(Z< -2.05) = 2P(Z<-2.05) = .0404$ (by symmetry)

What you calculated was $P(|Z|<2.05)$

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