A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a...

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.07 3.07 ounces with an allowable deviation of 0.05 0.05 ounces. The average weight of a bag of potato chips is supposed to be 5.03 5.03 ounces with an allowable deviation of 0.03 0.03 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.06 3.06 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.07 5.07 ounces. Which description closely matches the findings on the assembly line? Answer

The popcorn bag assembly line is closer to the specifications given because its z-score is closer to the standard mean than the potato chip bag assembly line.

The popcorn bag assembly line is closer to the specifications given because its z-score is further from the standard mean than the potato chip bag assembly line.

The potato chip bag assembly line is closer to the specifications given because its z-score is closer to the standard mean than the popcorn bag assembly line.

The potato chip bag assembly line is closer to the specifications given because its z-score is further from the standard mean than the popcorn bag assembly line.

Solutions

Expert Solution

Given,

The average weight of a bag of popcorn is supposed to be 3.07 ounces with an allowable deviation of 0.05 ounces

Bag of popcorn from the assembly line and it has a weight of 3.06 ounces

Z-score of Bag of popcorn with weight of 3.06 ounces = (3.06-3.07)/0.05 = -0.01/0.05 = -0.2

Absolute value of Z-score of Bag of popcorn with weight of 3.06 ounces = 0.2

The average weight of a bag of potato chips is supposed to be 5.03 ounces with an allowable deviation of 0.03 ounces

A bag of potato chips from the assembly line and it has a weight of 5.07 ounces

Z-score of A bag of potato chips with a weight of 5.07 ounces = (5.07-5.03)/0.03 = 0.04/0.03 = 1.33

As it can be observed that Z-score of Bag of popcorn : 0.2 < Z-score of A bag of potato chips 1.33; Hence the popcorn assembly line is closer to it's standard mean

Ans :

The popcorn bag assembly line is closer to the specifications given because its z-score is closer to the standard mean than the potato chip bag assembly line.

orchestra answered 1 year ago

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