Question

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?

Answer 1

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.