Stats - the Central Limit Theorem

Bottles ﬁlled by a certain machine are supposed to contain 12 oz of liquid. In fact the ﬁll volume is random with mean 12.01 oz and standard deviation 0.2 oz. What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz?

I feel like this should be something like 12.1-12 / sqrt(144), but that isn't right. Any help is appreciated.

• sqrt(144) is close. but it doesn't consider the original std of 0.2. try looking up the variance for the average (or x bar) Feb 19 '14 at 23:12

Hint: The standard deviation for the mean of $144$ samples is $1/12$ of the standard deviation for one sample. Thus, we compute the probability of being at least $\frac{0.01}{0.2/12}$ standard deviations below the mean.