Answer to Question #324146 in Statistics and Probability for pnkj

Question

A machine fills coffee powder in pouches, with an average of 200 gm and a standard deviation of 4 gm. Assuming that the coffee weight is normally distributed. Find the probability that a coffee pouch selected at random will contain the following quantity of a coffee: I) At least 200 gm. II) Between 200 to 206 gm

Answer 1

$I)\;p(x\geq 200)=p(z\geq \frac{200-200}{4})=p(z\geq0)=0.5\\ II)\; p(200<x<206)=p( \frac{200-200}{4}<z< \frac{206-200}{4})\\ =p(0<z<1.5)=0.4332$