Question

lilly stores her craft stickers in two containers. each container has 300 stickers of different colors. the box plots show the number of green stickers found in random samples of 30 stickers from each container. based on the data sets, can lilly expect more green stickers in container a or container b? about how many more? lilly can expect that container? has about? more green stickers.

Explanation:

Step1: Find the median of each box - plot

The median of a box - plot is the line inside the box.
For Container A: The median is \(20\) (since the line inside the box of Container A is at \(20\)).
For Container B: The median is \(14\) (since the line inside the box of Container B is at \(14\)).

Step2: Calculate the difference in medians

The formula for the difference is \(d=\text{Median of A}-\text{Median of B}\).
Substitute the values: \(d = 20 - 14=6\).
Since each sample is \(\frac{30}{300}=\frac{1}{10}\) of the container (because each container has \(300\) stickers and the sample size is \(30\)).
To find the difference in the number of green stickers in the whole containers, we use the proportion. If the difference in the sample (of size \(30\)) is \(6\), and let \(x\) be the difference in the container (of size \(300\)).
We set up the proportion \(\frac{6}{30}=\frac{x}{300}\).
Cross - multiply: \(30x=6\times300\).
Solve for \(x\): \(x = 60\).

Answer:

Lilly can expect that Container A has about \(60\) more green stickers.