Answer to Question #16583 in Statistics and Probability for Eric

Question #16583

Suppose X1, X2 are iid exponential random variables with mean 2. If we invoke the Central Limit Theorem and assume that Xn-bar is normally distributed, how large must n be to insure that P[|Xn bar - 2| < .01] > .95?
I first standardized this and used Chebychev's inequality to get that (1/n) *( var/epsilon squared) < .05 so (1/n) *( 1/.005 squared) < .05 therfore n>800,000 . However this is the same answer I got when I did not invoke the CLT so I did something wrong somewhere. Can you please point out the mistake?

The clock is ticking. The coffee is brewing. The stress intensifies. And all you’ve written in the past 15 minutes…

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