Boxes are labeled as containing 500 g of cereal. The machinefilling the boxes pr

Question

Boxes are labeled as containing 500 g of cereal. The machinefilling the boxes produces weights that are normally distributedwith standard deviation 12 g.
a) If the target weight is 500 g, what is the probability that themachine produces a box with less than 480 g of cereal?
b) Suppose a law states that no more than 5% of a manufacturer's cereal boxes can contain less than the stated weight of 500 g. Atwhat target weight should the manufacturer set its filling machine?

I got 4.7% on question A, which is the correct answer, however, i have no idea how to solve question B. I cannot use any computer programs, so a step-by-step solution would be nice.

Explanation / Answer

a.) If the target weight is 500 grams, what is the probability that the machine produces a box with less than 480 grams of cereal?

normalcdf(0,480,500,12) = .0478 = 4.78%

b.) Suppose a law states that no more than 5% of a manufacturer's cereal boxes can contain less than the stated weight of 500 grams. At what target weight should the manufacturer set its filling machine?

normalcdf(0,480,499,8,12) = .0503 = 5.03%
499.8 grams

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

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