Question

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.05 ounces with an allowable deviation of 0.04 ounces. The average weight of a bag of potato chips is supposed to be 5.01 ounces with an allowable deviation of 0.05 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 5.07 ounces. Which description closely matches the findings on the assembly line? Answer 4 Points Keypad

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.

Answer 1

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.

Explanation:

z- score for pop corn

average weight for a pop corn bag=3.05

Standard deviation for a pop corn bag=0.04

z=x-mean/standard deviation

z=3.03-3.05/0.04

z=-0.5

z- score for potato chips

average weight for a potato chips bag=5.01

Standard deviation for a potato chips bag=0.05

z=x-mean/standard deviation

z=5.07-5.01/0.05

z=1.2

As z-score for pop corn bag -0.5 is closer to standard mean i.e. 0 than the z-score for potato chips bag, so,

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.