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An automatic machine that fills bags of unpopped popcorn is operating properly if the weights are independently and normally distributed with a mean of 114 grams and a standard deviation of 4.9 grams. Find the probability that if 7 bags are randomly selected, their mean weight exceeds 115 grams.

  • statistics -

    Use z-scores:

    z = (x - mean)/(sd/√n)

    With your data:

    z = (115 - 114)/(4.9/√7)

    Finish the calculation.

    Next, check a z-table to find probability using the above z-score.

    I hope this will help get you started.

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