# A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of soap?

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.

What proportion of boxes is underweight (i.e. weigh less than 32 oz.)?

----> The answer is .0764 . How do I get here?

How heavy does a box have to be for it to be labeled overweight?

-----> The answer is 34.15 oz. Please show me how to solve this.

Thank you kindly.

• 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)