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, with a mean weight of 2 pounds, what must the standard deviation be? Assume that the box weights are normally distributed.
A) Approximately 0.05 pounds
B) -0.133 pounds
C) 1.144 pounds
D) None of the above

Question

Quizplus · Accepted Answer

To ensure no more than 3% of boxes weigh more than 2.10 pounds with a mean of 2 pounds, we use the Z-score formula: Z = (X - μ) / σ. For the top 3%, Z ≈ 1.88. Plugging in X = 2.10, μ = 2, we solve for σ ≈ 0.05 pounds.

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