Question

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?