# cumulative probabilities for standard normal density vs confidence interval

Lets say I have a 90% confidence interval. It's Z score is 1.645 (so 90% of values are between -1.645 and 1.645 standard deviations from the mean) and and it's got error margin of 5% in each tail of the snd curve. How come it's probability is between .9495 and .9505? Shouldn't probability be 90% or so?

Can someone explain to me why this isn't the case?

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Because P(z<= 1.645) implies you're looking at values in one of the tails. I've been trying to figure this out for hours and the answer just came to me. I'll vote to remove this questions if you guys think it's stupid... Or I'll add my own answer in 7 hours. – Nik Sep 12 '12 at 2:21