Is the following normallydistributed? Justify. Bottles of a popular cola are sup

Question

Is the following normallydistributed? Justify. Bottles of a popular cola are supposedto contain 300 milliliters of cola. There is some variationfrom bottle to bottle because the filling machinery is notperfectly precise. In a random sample of 50 bottles, the meanamount is 299.2 milliliters with standard deviation 4.6milliliters. I know normal distribution is bell shaped curve. And thatabout 33% data likes between one standard deviation of mean, 67% ofdata lies within 2 standard deviations of mean and about all thedata lies between 3 standard deviations of mean. however, how tovisualize this problem? I am confused. Help would beappreciated. Bottles of a popular cola are supposedto contain 300 milliliters of cola. There is some variationfrom bottle to bottle because the filling machinery is notperfectly precise. In a random sample of 50 bottles, the meanamount is 299.2 milliliters with standard deviation 4.6milliliters. I know normal distribution is bell shaped curve. And thatabout 33% data likes between one standard deviation of mean, 67% ofdata lies within 2 standard deviations of mean and about all thedata lies between 3 standard deviations of mean. however, how tovisualize this problem? I am confused. Help would beappreciated. I know normal distribution is bell shaped curve. And thatabout 33% data likes between one standard deviation of mean, 67% ofdata lies within 2 standard deviations of mean and about all thedata lies between 3 standard deviations of mean. however, how tovisualize this problem? I am confused. Help would beappreciated.

Explanation / Answer

This if a centering process where the machine is set to fill each bottle with 300ml of cola.  Because of setting inaccuracy each bottle filled may to be a little under or over this amount, but most of the bottles would be centered about 300ml.   The normal assumption for this process seems reasonable.

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