Answer to Question #289271 in Statistics and Probability for Anne

Question

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 992 mL and 998 mL?

Answer 1

μ=999mL

σ=5

P(992<X<998)=$P(\frac{992-999}{5}<Z<\frac{998-999}{5})\\ P(-1.4<Z<-0.2)\\ P(Z<-0.2)-p(Z<-1.4)\\ 0.4207-0.0808=0.3399$