Boxes are labeled as containing 600 g of cereal. The machine filling the boxes p

Question

Boxes are labeled as containing 600 g of cereal. The machine filling the boxes produces weights that are normally are distributed with standard deviation 9 g. (a) If the target weight is 600 g, what is the probability that the machine produces a box with less than 580 g of cereal? (b) Suppose a law states that no more than 2% of a manufacturer's cereal boxes can contain less than the stated weight of 600 g. At what target weight should the manufacturer set its filling machine? (Round your answer to the nearest gram.)

Explanation / Answer

a)for normal distribution zscore =(X-mean)/std deviaiton

hence P(X<580)= P(Z<(580-600)/9)=P(Z<-2.2222)=0.013

b)

for lowest 2 percentile ; z=-2.05375

hence corresponding target weight =600+2.05375*9=618.48 gm~619 gm

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.