Question

A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16. 5 oz. The boxes filled by the machine have weights that can be closely approximated by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is 0. 3 oz?

Answer 1

The boxes filled by the machine are underweight if the standard deviation is 0. 3 oz  is 0.62%

we are given a box of oatmean containing 16 oz, a  machine that fille the oatmeal boxes on an average  of 16.5 oz boxes and the boxes filled by the machine have weights that can be closely approximated by a normal curve, at last, we are given the standard deviation of  0. 3 oz .The formula we are referring to for calculating the z score is  

z = x- mean /standard deviation , where x is the observed value

So for the standard  value of  0.3 oz, z= 16-16.5/0.3 = -2.5

The probability for the  score -2.5 is s 0.0062 or 0.62%

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