I am trying to find the probability of the following question:
Cans of regular Coke are labeled as containing 12 oz. Statistics students weighed the contents of 7 randomly chosen cans, and found the mean weight to be 12.11 ounces.
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 0.1 oz. Find the probability that a sample of 7 cans will have a mean amount of at least 12.11 oz.
I am using the StatTrek Normal Distribution Calculator linked below. http://stattrek.com/online-calculator/normal.aspx
I'm plugging in the following values to the calculator listed above:
Normal random variable(x) = 7
Mean = 12.11
Standard Deviation = 0.1 (i.e. I have also tried plugging in Standard Deviation = .1/sqrt(7))
Probability = ?
Unfortunately, I am getting the incorrect answer of 0.00003. Not only this, but the calculator changes my random variable to 12.07. Can someone tell me what I'm plugging in wrong or is the above online calculator faulty, by any chance?
You need the standard error of the mean $\frac{\sigma}{\sqrt n}$ not $\sigma$