One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine...

[abako]

[FONT=&quot]One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with a standard deviation of 20 mg. What is the probability that the average caffeine in a sample of 25 bottles is no more than 390 milligrams?

Not sure how to start this problem, could you please give some hints. [/FONT][FONT=&quot]


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[HallsofIvy]

You are told "mean" and "standard deviation" so this is clearly a "normal distribution" problem. The mean is 400 and the standard deviation is 20 mg so the "standardized variable" is (390- 400)/20= -0.5 (390 is 1/2 standard deviations below the mean). Use a table of the standard normal distribution to look up the probability that z< -0.5.