Question

At her birthday party, Jayla wants to play a game where team members race through an obstacle course with bean bags on their heads. She bought a box of 100 bean bags in assorted colors to use in the game. She randomly selected 14 bean bags from the box and then put them back. Here are the colors she selected:

red, blue, green, blue, yellow, red, green, blue, red, yellow, red, green, blue, red
Based on the data, estimate how many red bean bags are in the box.
If necessary, round your answer to the nearest whole number.

Answer 1

Answer + Explanation:

To estimate how many red bean bags are in the box, we can use a sampling method called "balloting." Balloting is a way of estimating the number of items of a specific type in a larger population by taking a random sample and counting how many of that type are in the sample.

In this case, we have a population of 100 bean bags and a sample size of 14. We can calculate the sample proportion of red bean bags by dividing the number of red bean bags in the sample by the total number of bean bags in the sample, which gives:

(4/14) × 100% ≈ 28.6%

This means that, on average, we would expect 28.6% of the 100 bean bags in the box to be red. To estimate the actual number of red bean bags, we can multiply the sample proportion by the total number of bean bags in the box:

28.6% × 100 = 28.6

So the closest estimate for the number of red bean bags in the box is 29.

Note that this is just an estimate, and the actual number of red bean bags in the box may be higher or lower than the estimated value.

Answer 2

Jayla selected 14 bean bags randomly with replacement from a box of 100 bean bags, and 6 of them were red. To estimate how many red bean bags are in the box, we can use proportion:

Let's call "x" the number of red bean bags in the box. Then we can set up a proportion:

(red bean bags in the box) / (total bean bags in the box) = (red bean bags selected) / (total bean bags selected)

x / 100 = 6 / 14

Simplifying the right side, we get:

x / 100 = 3 / 7

Multiplying both sides by 100, we get:

x = 300 / 7

Rounding to the nearest whole number, we get:

x ≈ 43

Therefore, based on the data, we can estimate that there are approximately 43 red bean bags in the box.