# Interpreting confidence intervals

Suppose I have a $95 \%$ confidence interval for $\mu$ with population variance $\sigma^{2}$ known. It will be of the form $$[\bar{X}-1.96 \sigma/\sqrt{n}, \bar{X}+1.96 \sigma/\sqrt{n}]$$

The statistical interpretation of this is that $95\%$ of the confidence intervals will contain the true mean? I know individually, there is a $50\%$ chance for a confidence interval to contain the mean. But collectively, my above sentence is valid?

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possible duplicate question (c.f. stats.stackexchange.com/questions/11609/… ). It isn't clear how this question is distinct. –  Dikran Marsupial Jun 24 '11 at 19:03
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## merged by whuber♦Jun 24 '11 at 19:48

this question was merged with Clarification on interpreting confidence intervals? because it is an exact duplicate of that question.