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Jine · 2019年11月21日

问一道题:NO.PZ2017092702000107

问题如下:

A population has a non-normal distribution with mean µ and variance σ2. The sampling distribution of the sample mean computed from samples of large size from that population will have:

选项:

A.

the same distribution as the population distribution.

B.

its mean approximately equal to the population mean.

C.

its variance approximately equal to the population variance.

解释:

B is correct.

Given a population described by any probability distribution (normal or nonnormal) with finite variance, the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, with the mean approximately equal to the population mean, when the sample size is large.

请问老师A为什么是错的呢?不是说large就会都趋于正态分布吗?不就是same distribution吗?谢谢!

2 个答案

tearhr · 2020年02月18日

这道题可否这样理解:即使总体不服从正态分布,但是样本容量足够大,样本服从正态分布,所以样本均值=总体均值,样本方差=总体方差除以N。

星星_品职助教 · 2020年02月18日

可以这么理解,这个就是中心极限定理的解读

星星_品职助教 · 2019年11月21日

同学你好,

这道题考察的是中心极限定理的应用。中心极限定理说的是从“任意”分布中抽样,只要样本足够大,那么样本均值就服从正态分布。

对于这道题来说,题干中说明原总体是个非正态分布,而样本均值服从的是正态分布,所以这两个分布是不同的,就不能选择A。

large sample size在这里的用处是表明满足了中心极限定理的条件“N足够大”,所以才可以得出样本均值服从正态的结论。加油~


Jine · 2019年11月22日

样本均值服从的是正态分布?题目中哪里可以看出呢?The sampling distribution of the sample mean computed from samples of large size from that population will have:,这句话看不出来说sample是属于正态分布呢~麻烦星星再帮忙解释一下吧。谢谢!

星星_品职助教 · 2019年11月22日

这个是中心极限定理的结论,如果样本容量足够大(N>30),那么抽出来的样本的样本均值X bar就服从正态分布,均值就是总体均值,方差是总体方差除以N。 所以看到是sample mean的分布,样本容量又足够大,可以直接得出sample mean服从正态的结论~

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2022-12-08 15:35 1 · 回答

NO.PZ2017092702000107 问题如下 A population ha non-normstribution with meµ anvarianσ2. The sampling stribution of the sample mecomputefrom samples of large size from thpopulation will have: A.the same stribution the population stribution. B.its meapproximately equto the population mean. C.its varianapproximately equto the population variance. B is correct. Given a population scribeany probability stribution (normor nonnormal) with finite variance, the centrlimit theorem states ththe sampling stribution of the sample mewill approximately normal, with the meapproximately equto the population mean, when the sample size is large.给定具有有限方差的任何概率分布(正态或非正态)描述的总体,中心极限定理指出,当样本大小足够大的时候,样本均值为正态分布,其中样本均值等于总体均值。 RT

2022-09-18 13:05 2 · 回答

NO.PZ2017092702000107 这个题是不是应该放在中心极限定理部分?

2022-02-11 16:56 3 · 回答

    提问请问老师A和C哪里错了?谢谢您

2018-10-26 17:31 1 · 回答