Answer:
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
