A cereal manufacture has a machine that files the boxes. Boxes are labeled as 16 ounces, which is the target fill (x). The lawyers want to fill the boxes more to avoid lawsuits regarding under filling and the company president vetoes that plan, saying the company should be giving away less free cereal, not more. Her goal is to set the machine no higher than 16.2 ounces and have only 4% underweight boxes. The only way to accomplish this is to reduce the standard deviation. What standard deviation must the company achieve

σ = 0,11

Step-by-step explanation:

We assume the boxes filling process follows a Normal Distribution, then

z(score) = ( X - μ ) /σ     or   z(score) = ( μ - X ) /σ  

depending of the tail of the curve ( as we are evaluating boxes below mean we need to use the second equation )

where   μ  and σ are the mean and the standard deviation of the population

As the goal is to have boxes with no higher than 16,2 ou and only  4% of underweight boxes

4%   is 0,04   that should be the area under the bell shape curve then from z table we find z(s)

z(s) = - 1,75

z(s)  = ( μ - X )/σ

- 1,75 = ( 16,2 - 16 ) / σ

σ = 0,2 / 1,75

σ = 0,11

687.09 dollars       happy now

step-by-step explanation: 6870

1857 times .63 equals 1169.91 subtract that from 1857 you get 687.09