Question

An apple orchard's workers pick 14,446 apples in the month of October. A sample of 109 of these apples shows that 48 of them are damaged and bruised. What is the best estimate of the number of apples picked at the orchard in October that are bruised and damaged?

Answer 1

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.