A box contains 300 colored paper clips. Tony pulled 25 paper clips out at random and found 6 pink, 4 white, 10 yellow, and 5 blue clips in the sample

from the data. Tony predicts there are about 150 yellow paper clips in the entire box. Ia tony's prediction reasonable?

To determine if Tony's prediction is reasonable, we need to compare the ratio of yellow paper clips in the sample to the ratio in the entire box.

First, let's calculate the ratio of yellow paper clips in the sample. Tony pulled out a total of 25 paper clips, and out of those, 10 were yellow. The ratio is calculated as:

Yellow paper clips in sample / Total paper clips in sample = 10 / 25 = 2 / 5

Next, let's calculate the ratio of yellow paper clips in the entire box. Tony predicts there are about 150 yellow paper clips in the box, and the total number of paper clips in the box is 300. The ratio is calculated as:

Yellow paper clips in entire box / Total paper clips in entire box = 150 / 300 = 1 / 2

Comparing the two ratios, we find that the ratio in the sample (2/5) is not the same as the ratio in the entire box (1/2). This indicates that Tony's prediction may not be reasonable.

To make a more accurate prediction, we can use the proportion:

Yellow paper clips in sample / Total paper clips in sample = Yellow paper clips in entire box / Total paper clips in entire box

Plugging in the values we know:

10 / 25 = x / 300

Solving for x, we find:

x = (10 / 25) * 300 = 120

Therefore, based on the proportion calculation, we can estimate that there are approximately 120 yellow paper clips in the entire box.

Comparing this estimate with Tony's prediction of 150, it seems that Tony overestimated the number of yellow paper clips.