Question

Boxes are labeled as containing 600 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 8 g. (a) If the target weight is 600 g, what is the probability that the machine produces a box with less than 585 g of cereal? (Round your answer to three decimal places.)

Answer 1

Given $\mu =600$ and $\sigma =8$

$Z=\frac{x-\mu }{\sigma }=\frac{585-600}{8}=\frac{-15}{8}=-1.875$

$P(X< 585)=P(Z< -1.875)=0.0304$