A water bottling faclity has a mean bottling rate of 35.2 thousand bottles per hour with a standard deviation of 2.04 thousand bottles. A nearty cola botting facility has a mean botting rate of 26.9 thousand bottles per hour with a standard deviation of 1.51 thousand bottles. One Wednesday from noon to 100 pm . the warer borling facility bottled 37.4 thousand bottles of water, and the cola botting factity bottied 28.8 thousand boutles of cola. Which factiy hctered their efferey more siring that hour?

Answer
Keypad
Keybo ard Shartues
the water bottling facily
the cola botting facility
both increased their efficiency by the same amount
there is not enough information to determine

Question

A water bottling faclity has a mean bottling rate of 35.2 thousand bottles per hour with a standard deviation of 2.04 thousand bottles. A nearty cola botting facility has a mean botting rate of 26.9 thousand bottles per hour with a standard deviation of 1.51 thousand bottles. One Wednesday from noon to 100 pm . the warer borling facility bottled 37.4 thousand bottles of water, and the cola botting factity bottied 28.8 thousand boutles of cola. Which factiy hctered their efferey more siring that hour?

Answer
Keypad
Keybo ard Shartues
the water bottling facily
the cola botting facility
both increased their efficiency by the same amount
there is not enough information to determine

UpStudy AI · Accepted Answer

We start by comparing how many standard deviations each facility's performance is from its mean. This is done using the $$ z $$-score formula:

$$
z = \frac{\text{observed value} - \text{mean}}{\text{standard deviation}}
$$

**For the water bottling facility:**

- Mean rate: $$ 35.2 $$ thousand bottles/hour  
- Standard deviation: $$ 2.04 $$ thousand bottles  
- Observed rate: $$ 37.4 $$ thousand bottles

Calculate the $$ z $$-score:

$$
z_{\text{water}} = \frac{37.4 - 35.2}{2.04} = \frac{2.2}{2.04} \approx 1.08
$$

**For the cola bottling facility:**

- Mean rate: $$ 26.9 $$ thousand bottles/hour  
- Standard deviation: $$ 1.51 $$ thousand bottles  
- Observed rate: $$ 28.8 $$ thousand bottles

Calculate the $$ z $$-score:

$$
z_{\text{cola}} = \frac{28.8 - 26.9}{1.51} = \frac{1.9}{1.51} \approx 1.26
$$

**Comparison:**

- Water facility $$ z $$-score: approximately $$ 1.08 $$
- Cola facility $$ z $$-score: approximately $$ 1.26 $$

Since the cola bottling facility's performance is further above its mean (in terms of standard deviations) than the water bottling facility's performance, the cola facility improved its efficiency by a greater degree relative to its normal operating performance.

$$
\textbf{Answer: the cola bottling facility}
$$
The cola bottling facility increased its efficiency more than the water bottling facility that hour.

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