What is the total number of pieces in a mailing weighing 405.8750 pounds with a sample of 13 pieces weighing .6351 pounds?

To determine the total number of pieces in a mailing based on the given weight, the approach involves calculating the weight of a single piece and then dividing the total weight of the mailing by that weight.

First, you can find the average weight of a single piece by dividing the weight of the sample by the number of pieces in the sample. In this case, the sample weight is 0.6351 pounds, and there are 13 pieces in that sample. The calculation for the average weight of one piece would be:

[ \text{Average weight per piece} = \frac{0.6351 \text{ pounds}}{13 \text{ pieces}} \approx 0.0488 \text{ pounds per piece} ]

Next, to find the total number of pieces in the mailing, divide the total weight of the mailing (405.8750 pounds) by the average weight per piece:

[ \text{Total pieces} = \frac{405.8750 \text{ pounds}}{0.0488 \text{ pounds per piece}} ]

Carrying out this calculation gives approximately 8300 pieces.

Thus, choosing 8300 as the answer corresponds to accurately applying the concept of using sample data to