As part of a statistics project, a teacher brings a bag of marbles containing 600 white marbles and 400 red marbles. She tells the students the bag contains 1000 total marbles, and asks her students to determine how many red marbles are in the bag without counting them.
A student randomly draws 150 marbles from the bag. Of the 150 marbles, 63 are red.
1.Based on the sample, the student would estimate that _________ marbles in the bag were red.
63/150 * 1000 = ____
To estimate the number of red marbles in the bag based on the sample, we can use the concept of proportions.
The proportion of the number of red marbles in the sample to the total number of marbles in the sample should be equal to the proportion of the number of red marbles in the bag to the total number of marbles in the bag.
Let's calculate the estimated number of red marbles in the bag:
Proportion in the sample = Number of red marbles in the sample / Total number of marbles in the sample
Proportion in the sample = 63 / 150
We can set up a proportion equation:
Proportion in the sample = Proportion in the bag
63 / 150 = x / 1000
To solve for x, the estimated number of red marbles in the bag, we can cross-multiply and then divide:
(63 * 1000) / 150 = x
x = 420
Therefore, based on the sample, the student would estimate that 420 marbles in the bag were red.
To estimate the number of red marbles in the bag based on the sample of 150 marbles drawn, you can use a proportion.
First, calculate the proportion of red marbles in the sample:
Proportion of red marbles in the sample = (Number of red marbles in the sample) / (Total number of marbles in the sample)
In this case, the student drew 150 marbles and found that 63 of them were red:
Proportion of red marbles in the sample = 63 / 150 = 0.42
Next, use this proportion to estimate the number of red marbles in the entire bag.
Since the student has estimated that 42% of the sample is red, apply this proportion to the total number of marbles in the bag:
Estimated number of red marbles in the bag = (Proportion of red marbles in the sample) * (Total number of marbles in the bag)
In this case:
Estimated number of red marbles in the bag = 0.42 * 1000 = 420
Therefore, based on the sample, the student would estimate that there are 420 red marbles in the bag.