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.
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.