Question

A company produces packets of soap powder labeled "Giant Size 16 oz." The actual weight of soap powder in such a box has a Normal distribution with a mean of 17 oz and a standard deviation of 0.9 oz. To avoid dissatisfied customers, a box of soap is considered underweight if it weighs less than 16 oz. To avoid losing money, the top 5% (the heaviest 5%) is labeled overweight. How heavy does a box have to be in order for the box to be labeled overweight??

Answer 1

It is given that the weight of soap powder has a Normal distribution with .

It is given that the top 5% is labeled overweight. The top 5% means

P(Z>?)=0.05.

We can get the value of ? from tables/technoogy that is NORM.S.INV(0.95) of EXCEL function, the value is 1.6449,

ie

  

  

Therefore, a box have to be more than 18.48 oz in order for the box to be labeled overweight.