Question

# Question #11: A manufacturer makes bags of popcorn and bags of potato chips. The average weight...

Question #11: 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 0.03 ounces. The average weight of a bag of potato chips is supposed to be 5.08 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 3.02 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?

2 Points

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.
2. 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.
3. 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.
4. 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.

Solution :

Given that ,

mean = = 3.06 (popcorn)

standard deviation = = 0.03

x = 3.02

Using z-score formula,

z = x - /

z = 3.02 - 3.06 / 0.03

z = -1.33 (popcorn)

mean = = 5.08 (potato)

standard deviation = = 0.05

x = 5.07

Using z-score formula,

z = x - /

z = 5.07 - 5.08 / 0.05

z = -0.20 (potato)

correct option is,

3. 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.