Which of the following is NOT a result of the Central Limit Theorem? Choose the correct answer below.&nbsp;a) As the sample size increases, the distribution of the sample means x-bar will approach a normal distribution.b) The distribution of the sample data will approach a normal distribution as the sample size increases.&nbsp;c) The variance of all sample means is the population variance divided by the square root of the sample size.d) The mean of all sample means is the population mean&nbsp;μ

Question

Which of the following is NOT a result of the Central Limit​ Theorem? Choose the correct answer below.&amp;nbsp;a) As the sample size increases, the distribution of the sample means x-bar will approach a normal distribution.b) The distribution of the sample data will approach a normal distribution as the sample size increases.&amp;nbsp;c) The variance of all sample means is the population variance divided by the square root of the sample size.d) The mean of all sample means is the population mean&amp;nbsp;μ

Elberte · Accepted Answer

Step 1&amp;nbsp;The options below are not correct&amp;nbsp;As the sample size grows, the distribution of the sample mean becomes more normal. The standard deviation of all sample means is the ratio of the population standard deviation to the square root of sample size, moreover the expected value of all sample means is equal to the population mean.&amp;nbsp;When the sample size sufficiently large then the distribution of sample mean leads to normal and the expected value of all sample means equal to population mean. The standard deviation of all sample means is equal to the population standard deviation divided by the square root of sample size.&amp;nbsp;Step 2&amp;nbsp;The correct option is identified below:&amp;nbsp;When sample size increases the distribution of sample data will not follow normal distribution but the average of sample mean leads normal.&amp;nbsp;The distribution of the sample data will approach a normal distribution as the sample size increases is not a conclusion of central limit theorem.&amp;nbsp;According to central limit theorem the distribution of sample data does not follow normal distribution as the sample size increases or decreases but the average of sample mean follows normal distribution.

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. a) The distribution of the sample means x ov

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New Questions in Calculus 1