A bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What proportion of bottles have Volumes less than 1,015 mL?
A) 1.0000
B) 0.9082
C) 0.6293
D) 0.9251

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the volume using the formula:

z = (x - μ) / σ

where x is the value we want to find the proportion for (in this case, 1,015 mL), μ is the mean (1,007 mL), and σ is the standard deviation (6 mL).

z = (1,015 - 1,007) / 6 = 1.33

We then use a standard normal table (or calculator) to find the proportion of bottles with volumes less than 1,015 mL, which is the area to the left of z = 1.33.

Using a standard normal table or calculator, we find that the proportion is approximately 0.9082.

Therefore, the best choice is B, which gives the correct proportion of bottles with volumes less than 1,015 mL.

A Bottler of Drinking Water Fills Plastic Bottles with a Mean