A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of soap powder in such a box has a Normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight.. Reference: Ref 3-5. . What proportion of boxes is underweight (i.e., weigh less than 32 oz)?. A..0764. B..2420. C..7580. D..9236.
z=(x-mu)/sd z=(32-33)/.7 z= -1.43 look this up in z score table and you get .4236. This is the area above a weigth of 32 and below the mean weight of 33. So the proportion that are underweight = .5 - .4236 = .0764
z=(x-mu)/sd 1.645=(x-33)/.7 Solving for x gives 34.15 (we get 1.65 by finding the area above the mean of .4500 in the table. Bottom half (.5) + .4500 = .95)
Therefore, the answer would be letter A. 0.0764.
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