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?

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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-scores for each facility based on their mean and standard deviation.

For the water bottling facility:
z = (X - μ) / σ
where X = 35.6, μ = 34.1, and σ = 2.13
z = (35.6 - 34.1) / 2.13
z = 0.70

For the cola bottling facility:
z = (X - μ) / σ
where X = 26.4, μ = 25.7, and σ = 1.63
z = (26.4 - 25.7) / 1.63
z = 0.43

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