To determine the weight of the fourth package, we follow these steps:
1. Calculate the total weight of all packages combined:
Given the mean (average) weight of the packages is 2.5 pounds and there are 4 packages, we first find the total weight of all the packages combined.
[tex]\[
\text{Total weight} = \text{Mean weight} \times \text{Number of packages} = 2.5 \times 4 = 10 \text{ pounds}
\][/tex]
2. Sum the weights of the known packages:
We know the weights of three of the packages: 1.8 pounds, 3.2 pounds, and 2.7 pounds. We sum these weights to find the total weight of the known packages.
[tex]\[
\text{Sum of known weights} = 1.8 + 3.2 + 2.7 = 7.7 \text{ pounds}
\][/tex]
3. Find the weight of the fourth package:
To find the weight of the fourth package, we subtract the sum of the weights of the known packages from the total weight of all packages combined.
[tex]\[
\text{Weight of the fourth package} = \text{Total weight} - \text{Sum of known weights} = 10 - 7.7 = 2.3 \text{ pounds}
\][/tex]
4. Verify with the given options:
- 2.3
- 2.8
- 3.3
The weight of the fourth package is 2.3 pounds, which is one of the given options.
Thus, the weight of the fourth package is 2.3 pounds.
