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.

Answer 1

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.