the average diameter of sand dollars on a certain island is 3.00 centimeters wit

Question

the average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation oof 0.70 centimeters.  A. if 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.790 centimeters.  Use the Central Limit Theorem and assume that the variable is normally distributed.      B.  What if 25 sand dollars were chosen at random?

Explanation / Answer

X~Normal (=3, =0.7) (a) n=9 P(xbar > 2.79) = P( (xbar-)/(/n) >(2.79-3)/(0.7/sqrt(9)) ) =P(Z>-0.9) = 0.8159 (b) n=25 P(xbar > 2.79) = P( (xbar-)/(/n) >(2.79-3)/(0.7/sqrt(25)) ) = P(Z> -1.5) =0.9332

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