Avery randomly selects 50 colored pencils from a basket and finds that 2 are not sharpened. If the basket contains 300 colored pencils, how many would you expect to be unsharpened?

Question

12
20
2
120

Answer 1

To find the expected number of unsharpened colored pencils in the basket, we can use the proportion of unsharpened pencils in the sample.

From Avery's selection, she found that out of 50 pencils, 2 were not sharpened. That means the proportion of unsharpened pencils in her sample is:

\[ \text{Proportion of unsharpened pencils} = \frac{2}{50} = 0.04 \]

Now, we can use this proportion to estimate the number of unsharpened pencils in the entire basket of 300 colored pencils:

\[ \text{Expected number of unsharpened pencils} = \text{Proportion of unsharpened pencils} \times \text{Total number of pencils} \]

\[ \text{Expected number of unsharpened pencils} = 0.04 \times 300 = 12 \]

So, the expected number of unsharpened colored pencils in the basket is 12.