Answer:
Coefficient of variation (weight) = 15%
Coefficient of variation (volume) = 25%
Step-by-step explanation:
Let's begin by listing out the given information:
Population = 200, Average weight = 26 lb,
standard deviation (weight) = 3.9 lb,
Average volume = 8.8 ft³,
standard deviation (volume) = 2.2 ft³
Based on the data given, the manager will have to make a deduction by comparing the relative scatter of both variables due to the different units of measuring weight (pounds) and volume (cubic feet).
To compare the variation of the weight and volume, we use the coefficient of variation given by the formula:
Coefficient of Variation = (Standard deviation ÷ Mean) * 100%
⇒ = (σ ÷ μ) * 100%
For weight
σ = 3.9 lb, μ = 26 lb
(weight) = (3.9 ÷ 26.0) * 100% = 15%
(weight) = <u>15</u>%
For volume
σ = 2.2 ft³, μ = 8.8 ft³
(volume) = (2.2 ÷ 8.8) * 100% = 25%
(volume) = <u>25</u>%
∴ <u>the relative variation of the volume of the package is greater than that of the weight of the package</u>