Find the probability that a sample of 7 cans will have a mean amount of at least...

Cans of regular Coke are labeled as containing 12 oz.
Statistics students weighted the content of 7 randomly chosen cans, and found the mean weight to be 12.15.
Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.09 oz. Find the probability that a sample of 7 cans will have a mean amount of at least 12.15oz

Let X be amount on oz. of regular Coke

X ∼ n(12; 0.09)

n = 7

Xmean = 12.15

Xmean ∼ n(12; 0.09/sqrt(7))

0.09/sqrt(7) = 0.03401680257

P(Xmean ≥ 12.15) = P((Xmean - 12)/0.03401680257 ≥ (12.15 - 12)/0.03401680257) = P(Z ≥ 4.41) = 0