A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters(mL)and standard deviation 5 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes less than 995 mL?
A)0.5793
B)0.9974
C)0.5596
D)1.0000

Question

Quizplus · Accepted Answer

To find the proportion of bottles with volumes less than 995 mL, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (995 mL), μ is the mean (994 mL), and σ is the standard deviation (5 mL). Calculating the Z-score gives Z = (995 - 994) / 5 = 0.2. Looking up 0.2 in a standard normal distribution table or using a calculator gives a proportion of approximately 0.5793.

A Bottler of Drinking Water Fills Plastic Bottles with a Mean