Question

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.03 ounces with an allowable deviation of 0.03 ounces. The average weight of a bag of potato chips is supposed to be 5.06 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 3.08 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.02 ounces. Which description closely matches the findings on the assembly line?

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

Answer 1

For bag of popcorn:

Here we have

The z-score for X = 3.08 is

For bag of potato chips:

Here we have

The z-score for X = 5.02 is

Correct option:

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.