Homework SourseThe makers of sweet things candy sell their candy by the box
The makers of sweet things candy sell their candy by the box. Based on company policy, the mean Target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3% of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.
The makers of sweet things candy sell their candy by the box. Based on company policy, the mean Target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3% of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.
Solution
The makers of sweet things candy sell their candy by the box. Based on company policy, the mean Target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3% of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.
Z value for top 3% = 1.881
(2.1-mean)/0.13 = 1.881
2.1-mean =0.24453
Mean = 2.1-0.24453 =1.85547
The required mean weight = 1.8555 pounds
