A quality supervisor for a factory that makes cell phone cases examines a sample of 46 cases. She finds that 8 cases are the wrong size. Which is the best prediction of the number of cases that will be the wrong size in a shipment of 3,000?

A.)410

B.)475

C.)506

D.)522

8/46 = W/3000

Solve for W.

The answer is 522

To make the best prediction of the number of cases that will be the wrong size in a shipment of 3,000, we can use the concept of proportions.

First, calculate the proportion of cases in the sample that are the wrong size:
Proportion of wrong-sized cases in the sample = (Number of wrong-sized cases) / (Total number of cases in the sample)
Proportion of wrong-sized cases in the sample = 8 / 46 = 0.1739

Next, use this proportion to estimate the number of wrong-sized cases in the shipment of 3,000.
Estimated number of wrong-sized cases in the shipment = (Proportion of wrong-sized cases in the sample) * (Total number of cases in the shipment)
Estimated number of wrong-sized cases in the shipment = 0.1739 * 3,000 = 521.7

Since we can't have a fractional number of cases, we need to round the estimate to the nearest whole number. Rounding the estimate of 521.7 gives us 522.

Therefore, the best prediction of the number of cases that will be the wrong size in a shipment of 3,000 is:
D.) 522