Certainly! Let's break down the problem step-by-step to find out the mean weight of the other 5 parcels.
1. Total Weight of All Parcels:
First, we need to find the total weight of all 8 parcels. The mean weight of the parcels is given as 2.5 kg, and there are 8 parcels in total. Hence, the total weight of all parcels can be calculated as:
[tex]\[
\text{Total weight of all parcels} = \text{Mean weight} \times \text{Number of parcels} = 2.5 \text{ kg} \times 8 = 20 \text{ kg}
\][/tex]
2. Total Weight of the First 3 Parcels:
Next, we need to find the total weight of the first 3 parcels. The mean weight of these 3 parcels is given as 2 kg. Using this information, we can calculate the total weight of the first 3 parcels as:
[tex]\[
\text{Total weight of the first 3 parcels} = \text{Mean weight of the first 3 parcels} \times 3 = 2 \text{ kg} \times 3 = 6 \text{ kg}
\][/tex]
3. Total Weight of the Remaining 5 Parcels:
Now, to find the total weight of the remaining 5 parcels, we subtract the total weight of the first 3 parcels from the total weight of all parcels:
[tex]\[
\text{Total weight of the remaining 5 parcels} = \text{Total weight of all parcels} - \text{Total weight of the first 3 parcels} = 20 \text{ kg} - 6 \text{ kg} = 14 \text{ kg}
\][/tex]
4. Mean Weight of the Remaining 5 Parcels:
Finally, we need to determine the mean weight of the remaining 5 parcels. This can be found by dividing the total weight of the remaining 5 parcels by the number of these parcels:
[tex]\[
\text{Mean weight of the remaining 5 parcels} = \frac{\text{Total weight of the remaining 5 parcels}}{5} = \frac{14 \text{ kg}}{5} = 2.8 \text{ kg}
\][/tex]
Hence, the mean weight of the other 5 parcels is 2.8 kg.
