# Thread: finding value of z0

1. ## finding value of z0

P(|z| > z0) = 0.10

Find z0.

I think the answer is z0 = 1.28, however I'm not sure how to get that. The first time I did it, I got 1.645, because I did 0.5 - 0.1. I know that is not correct, but am not clear on the logic of getting 1.28.

Any help would be appreciated.

Thanks

2. Originally Posted by toronto416
P(|z| > z0) = 0.10

Find z0.

I think the answer is z0 = 1.28, however I'm not sure how to get that. The first time I did it, I got 1.645, because I did 0.5 - 0.1. I know that is not correct, but am not clear on the logic of getting 1.28.

Any help would be appreciated.

Thanks
I assume Z is a standard normal random variable.
P(|z| > z0) = 0.10 => P(|z| < z0) = 0.90
=>
P(z < -1*z0) = P(z > z0) = 0.05 ( both the tail probability will be 0.05 & Most of the table/prob chart are designed in this fashion)
&
P[ -1.645 < Z <1.645 ] = 0.90
(& P[-1.28 <Z<1.28 ] =0.80 )

See the below link for the normal probability table.
http://math2.org/math/stat/distributions/z-dist.htm

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