A manufacturer makes bags of popcorn and bags of potato chips. the average weight of a bag of popcorn is supposed to be 3.02 ounces with an allowable deviation of 0.02 ounces. the average weight of a bag of potato chips is supposed to be 5.03 ounces with an allowable deviation of 0.04 ounces. a factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.03 ounces. then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.06 ounces. which description closely matches the findings on the assembly line?

If these were the given choices:

A. 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.

B. 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.

C. 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.

D. 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.

My answer is: A. 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.

Given:

Ave. weight of a bag of popcorn - 3.02 oz

allowable deviation - 0.02 oz

Ave. weight of a bag of potato chips - 5.03 oz

allowable deviation - 0.04 oz

Actual weight of bag of popcorn - 3.03 oz

Actual weight of bag of potato chips - 5.06 oz

The allowable deviation is very minimal in a bag of popcorn thus its z-score is nearer to the standard mean as compared to the bag of potato chips.