To determine the expected number of damaged jewelry pieces when Mrs. Harmon orders 5,500 pieces, we first need to calculate the damage rate based on the initial shipment.
In the initial shipment of 500 jewelry pieces, 15 pieces are damaged. We can calculate the damage rate as follows:
\[ \text{Damage rate} = \frac{\text{Number of damaged pieces}}{\text{Total number of pieces}} = \frac{15}{500} = 0.03 \]
This means that 3% of the jewelry pieces are expected to be damaged.
Now, to find out how many jewelry pieces are expected to be damaged in an order of 5,500 pieces, we can use this damage rate:
\[ \text{Expected number of damaged pieces} = \text{Damage rate} \times \text{Total number of pieces ordered} \] \[ \text{Expected number of damaged pieces} = 0.03 \times 5500 = 165 \]
Therefore, Mrs. Harmon should expect approximately 165 jewelry pieces to be damaged from her order of 5,500 pieces.