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 percent 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.
A) Just over 2 pounds
B) Approximately 2.33 pounds
C) Nearly 1.27 pounds
D) Approximately 1.86 pounds

Question

Quizplus · Accepted Answer

To ensure that only 3% of boxes exceed 2.10 pounds, we use the z-score for 97th percentile, which is approximately 1.88. Using the formula: mean + z * standard deviation = 2.10, we solve for the mean: mean = 2.10 - (1.88 * 0.13) ≈ 1.86 pounds.

The Makers of Sweet-Things Candy Sell Their Candy by the Box