Question

Identify characteristics of the shape of a sampling distribution using the central limit theorem. if repeated independent samples of yogurt sales were taken, according to the central limit theorem, the mean of those repeated samples would tend to be normally distributed if the sample size is large enough. the histogram for the yogurt sales is shown here. select the reason why the central limit theorem can be applied.

a.) the samples are large enough, independently drawn, and done repeatedly.
b.) the sample size features 50 or more observations.
c.) the data distribution is skewed positively.
d.) the data distribution is skewed negatively.

Answer 1

The reason the Central Limit Theorem can be applied to yogurt sales data is that the samples are large enough, independently drawn, and done repeatedly, which satisfies the theorem's conditions.

Step-by-step explanation:

The Central Limit Theorem (CLT) is fundamental in the field of statistics and it states that if you have a sufficiently large sample size, the distribution of sample means will approximate a normal distribution, regardless of the population's original distribution.

When applying the CLT to yogurt sales data, the ability to predict that the mean of repeated samples will be normally distributed is dependent on a few conditions. The distribution's approach to normality is based on the samples being large enough, drawn independently, and done repeatedly.

Selecting the correct reason for the application of the CLT to yogurt sales, we would consider that the samples must meet specific criteria to justify the theorem's use.

These criteria include the sample size being sufficiently large (usually n>30), the samples being independently drawn from the population, and the sample process repeated a number of times to establish the distribution of sample means.

Therefore, the answer to why the Central Limit Theorem can be applied is because a.) the samples are large enough, independently drawn, and done repeatedly.