Question

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 34.9 thousand bottles of water, and the cola bottling facility bottled 26.8 thousand bottles of cola. Which facility increased their efficiency more during that hour

Answer 1

Using z-scores, we have that due to the higher z-score, the water bottling facility increased their efficiency more during that hour.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.  

In this problem, the facility with the higher z-score increased their efficiency more during that hour.

For the water bottling facility, we have that $\mu = 33.5, \sigma = 1.92, X = 34.9$, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34.9 - 33.5}{1.92}$

$Z = 0.73$

For the cola bottling facility, we have that $\mu = 26.2, \sigma = 1.42, X = 26.8$, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26.8 - 26.2}{1.42}$

$Z = 0.42$

Due to the higher z-score, the water bottling facility increased their efficiency more during that hour.

A similar problem is given at https://brainly.com/question/24663213