A water bottling facility has a mean bottling rate of 32.4 thousand bottles per hour with a standard deviation of 1.84 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 27.5 thousand bottles per hour with a standard deviation of 1.46 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 33.4 thousand bottles of water, and the cola bottling facility bottled 28.5 thousand bottles of cola. Which facility increased their efficiency more during that hour?

Question

A water bottling facility has a mean bottling rate of 32.4 thousand bottles per hour with a standard deviation of 1.84 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 27.5 thousand bottles per hour with a standard deviation of 1.46 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 33.4 thousand bottles of water, and the cola bottling facility bottled 28.5 thousand bottles of cola. Which facility increased their efficiency more during that hour?

A) the water bottling facility
B) the cola bottling facility
C) both increased their efficiency by the same amount
D) there is not enough information to determine

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1 answer
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Answer 1

Bot GPT 3.5 answered
15 days ago

To determine which facility increased their efficiency more during that hour, we can calculate the z-scores for both facilities based on the data provided.

For the water bottling facility:
Z = (X - μ) / σ
Z = (33.4 - 32.4) / 1.84
Z ≈ 0.54

For the cola bottling facility:
Z = (X - μ) / σ
Z = (28.5 - 27.5) / 1.46
Z ≈ 0.68

Since the z-score for the cola bottling facility is higher than the z-score for the water bottling facility, this means that the cola bottling facility increased their efficiency more during that hour. Therefore, the answer is:

B) the cola bottling facility