Question

A cereal manufacturer has a machine that fills the boxes. Boxes are labeled “16 ounces”, so the company wants to have that much cereal in each box, but since no packaging process is perfect, there will be minor variations. If the machine is set at exactly 16 ounces and the Normal model applies, then about ½ the boxes will be underweight, making consumers unhappy and exposing the company to bad publicity and possible lawsuits. To prevent underweight boxes, the manufacturer has to set the mean a little higher than 16 ounces. Specifically, this machine fills boxes according a N(16.5, 0.3) normal model. Use this model to answer the following question. How full does a box have to be to be in the top 12% of heaviest boxes? Choose the range that contains the correct answer.

Between 16.5 and 16.6 ounces. Between 16.6 and 16.7 ounces. Between 16.7 and 16.8 ounces. Between 16.8 and 16.9 ounces. Between 16.9 and 17.0 ounces.

Answer 1

Solution:-

Given that,

mean = = 16.5

standard deviation = = 0.3

Using standard normal table,

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12  

= P(Z < z) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 1.17 ) = 0.88  

z = 1.17

Using z-score formula,

x = z * +

x = 1.17 * 0.3 + 16.5

x = 16.9

Between 16.9 and 17.0 ounces.