M&M’s The candy company claims that 10% of the M&M’s it produces are green. Suppose the
candies are packed at random into small bags containing about 25 M&M’s per bag. A class of
elementary students learning about percentages opens several bags, counts the various colors, and
calculates the proportion that are green. Simultaneously, a second class performs the same
investigation but their bags contain about 50 M&M’s per bag.
Which class (large bags or small bags) can use the CLT and why?
I don't understand this can you even use the cental limit theorem for this? and how?
You're stupid
Yes, the Central Limit Theorem (CLT) can be used in this scenario. The CLT states that for a large enough sample size, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution.
In this case, the CLT can be applied because the elementary students are counting the proportion of green M&M's in multiple bags. When the number of bags sampled is sufficiently large, the distribution of the sample proportions will converge towards a normal distribution.
The class with the larger bags (containing about 50 M&M's per bag) is more likely to meet the requirements for the CLT. This is because a larger sample size will lead to a larger number of M&M's being counted, thus increasing the probability of meeting the condition of a sufficiently large sample size.
The Central Limit Theorem (CLT) states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
In this scenario, we have two classes conducting investigations with different bag sizes, one with small bags (around 25 M&M's per bag) and the other with large bags (around 50 M&M's per bag).
The question is, which class can use the CLT to analyze their results?
To determine whether the CLT can be applied, we need to consider the sample sizes. As a general rule of thumb, the CLT holds when the sample size is reasonably large (ideally, greater than 30).
In this case, the small bag class has a sample size (around 25 M&M's per bag) that may not meet the criteria for a large enough sample size to apply the CLT. The sample size is relatively small, and the distribution of the proportions of green M&M's may not have a normal distribution. Therefore, the small bag class may not be able to use the CLT.
On the other hand, the large bag class has a sample size (around 50 M&M's per bag) that is reasonably large. With a larger sample size, the proportions of green M&M's in each bag are more likely to follow a normal distribution. Therefore, the large bag class can use the CLT to analyze their results.
In summary, the class with the large bags (around 50 M&M's per bag) can use the CLT because their sample size is reasonably large, whereas the class with the small bags may not be able to use the CLT due to a smaller sample size.