Question
Random Sampling Quick Check
3 of 53 of 5 Items
Question
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?(1 point)
Responses
20
20
12
12
120
120
2
Answers
GPT-4o mini
To determine how many unsharpened colored pencils you would expect in the entire basket of 300 pencils, you can set up a proportion based on the sample that Avery drew.
In Avery's sample of 50 colored pencils, 2 were unsharpened. This gives a proportion of:
\[
\frac{2 \text{ unsharpened}}{50 \text{ total}} = \frac{1 \text{ unsharpened}}{25 \text{ total}}
\]
Now, to find out how many unsharpened pencils would be expected in the full basket of 300 pencils, you can use this ratio:
\[
\text{Expected unsharpened} = \left(\frac{1}{25}\right) \times 300 = 12
\]
So, the expected number of unsharpened colored pencils in the basket of 300 is **12**.
In Avery's sample of 50 colored pencils, 2 were unsharpened. This gives a proportion of:
\[
\frac{2 \text{ unsharpened}}{50 \text{ total}} = \frac{1 \text{ unsharpened}}{25 \text{ total}}
\]
Now, to find out how many unsharpened pencils would be expected in the full basket of 300 pencils, you can use this ratio:
\[
\text{Expected unsharpened} = \left(\frac{1}{25}\right) \times 300 = 12
\]
So, the expected number of unsharpened colored pencils in the basket of 300 is **12**.