To estimate the number of apples picked at the orchard in October that are bruised and damaged, we can use the concept of proportion.
We know that 48 out of a sample of 109 apples were damaged and bruised. We can set up a proportion to find the estimate:
Number of damaged and bruised apples / Total number of apples = Number of damaged and bruised apples in the sample / Total number of apples in the sample
Let's denote the total number of apples picked in October as "x."
48 / x = 109 / 14,446
To solve for x, we can cross-multiply:
48 * 14,446 = 109 * x
692,208 = 109x
Dividing both sides by 109:
x = 6,348
Therefore, the best estimate of the number of apples picked at the orchard in October that are bruised and damaged is approximately 6,348 apples.