A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 35.6 thousand bottles of water, and the cola bottling facility bottled 26.4 thousand bottles of cola. Which facility increased their efficiency more during that hour?

Question

A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 35.6 thousand bottles of water, and the cola bottling facility bottled 26.4 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
14 days ago

To determine which facility increased their efficiency more during that hour, we can calculate the Z-score for each facility's bottling rate during that hour.

For the water bottling facility:
Z = (Observed bottling rate - Mean bottling rate) / Standard deviation
Z = (35.6 - 34.1) / 2.13
Z = 1.409

For the cola bottling facility:
Z = (Observed bottling rate - Mean bottling rate) / Standard deviation
Z = (26.4 - 25.7) / 1.63
Z = 0.429

Since the Z-score for the water bottling facility is larger, it means that the water bottling facility increased their efficiency more during that hour compared to the cola bottling facility. Therefore, the answer is:
A) the water bottling facility.