The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. The company
Receives complaints from consumers who actually measure the amount of soda in the cans and
Claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans
Contain less than the advertised 12 ounces of soda?
A).9332
B).5668
C).4332
D).0668

Question

Quizplus · Accepted Answer

To find the proportion of soda cans that contain less than the advertised 12 ounces, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (12 ounces), $\mu$ is the mean (12.45 ounces), and $\sigma$ is the standard deviation (0.30 ounce). Plugging in the values, we get $Z = \frac{12 - 12.45}{0.30} = -1.5$. Looking up -1.5 on the standard normal distribution table or using a calculator gives us a proportion of approximately 0.0668. This means about 6.68% of the cans contain less than the advertised 12 ounces.

The Volume of Soda a Dispensing Machine Pours into a 12-Ounce