Question

A bottler of drinking water fills plastic bottles with a mean volume of 1,000 milliliters (mL) and standard deviation of 7. The fill volumes are normally distributed. What is the probability that a bottle has a volume between 996ml and 1,002ml?

Answer 1

$μ = 1000 \; mL \\ σ = 7 \\ P(996 < X < 1002) = P(\frac{996-1000}{7}<Z< \frac{1002-1000}{7}) \\ = P(-0.571<Z<0.285) \\ = P(Z<0.285) -P(Z<-0.571) \\ = 0.6121 -0.2839 \\ = 0.3282$