If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means

Question

BlackTom AI · Accepted Answer

Consider the statement: If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means will reflect certain probabilistic principles.
Option 1: 'will always be normal because we do not know the distribution of the population.' This is not correct. The distribution of sample means is not guaranteed to be normal in every population, especially if the population is highly skewed or has heavy tails; the guarantee comes from the Central Limit Theorem under appropriate conditions, not from unknown population shape alone.
Option 2: 'will always be normal because the sample mean is always normal.' This is misleading. The sample mean itself is a random variable whose distribution can be approximately normal for large enough samples, but it is not inherently always normal for any sample size or population; the approximation depends on sample size and population characteristics.
Option 3: 'will be approximately normal because of the Central Limit Theorem.' This aligns with the Central Limit Theorem, which states that the distribution of the sample mean tends toward normality as the sample size increases, here n = 40, which is typically sufficient for many populations to yield an approximately normal distribution of the sample mean.
Option 4: 'will not be normal because we do not know the distribution of the population.' This overstates the limitation. While the population distribution matters, the CLT ensures approximate normality of the sample mean for reasonably large samples regardless of the population’s shape (provided certain conditions are met), so we are not guaranteed non-normality.
In summary, the most accurate assertion among the options is that the distribution of the sample means will be approximately normal due to the Central Limit Theorem, given a sample size of 40 from an infinite population and repeated sampling.

If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means

查看解析

登录即可查看完整答案

类似问题

The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

How does the normal distribution emerge? Pick between A , B and C

Can we assume that the distribution of mean lead concentrations in blood collected from repeated samples of 52 police officers to be normal?

Check the conditions required to complete this test. Specifically, is the sampling distribution of average differences approximately normally distributed?

Which of the following is incorrect about the sampling distribution of the sample mean using the Central Limit Theorem?[Fill in the blank]

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单