A bottler of drinking water fills plastic bottles with a mean volume of 1001 milliliters (ml) and standard deviation of 6 ml. the fill volumes are normally distributed. what proportion of bottles have volumes less than 1001 ml?

The formula for z-score is:

z-score = (X - μ) / σ

where,

X = sample

μ = mean = 1001

σ = standard deviation = 6

Since we are looking for volumes less than 1001 mL, let us use 1000.5 mL for X.

z-score = (1000.5 - 1001) / 6

z-score = - 0.083

Referring to the standard distribution table for z-test, this corresponds to:

p = 0.4681

So 46.81% of the bottles are less than 1001 mL.