Question

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.06 ounces with an allowable deviation of 0.02 ounces. The average weight of a bag of potato chips is supposed to be 5.05 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 1

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

Explanation:

Popcorn mean= μ`1= 3.06

Popcorn St. Dev= σ1= 0.02

Potato Mean= μ`2= 5.05

Potato St. Dev= σ2= 0.05

Finding the z score

z= x- u / σ

Popcorn z= 3.06- 3.03/0.02= 1.5

Potato Z= 5.05-5.07/0.05= -0.4

The mean is taken to be at zero ( 0) therefore difference of 0.4 is less than a difference of 1.5

Choice 3 is the best option .