Central Limit Theorem for sampling distribution is valid only when:Select one:a. Large samples drawn from any independent and identically distributed populationb. The population follows normal distributionc. Samples are drawn from any independent and identically distributed populationd. The population follows a normal distribution and the sample size should be at least 30
Question
Central Limit Theorem for sampling distribution is valid only when:Select one:a. Large samples drawn from any independent and identically distributed populationb. The population follows normal distributionc. Samples are drawn from any independent and identically distributed populationd. The population follows a normal distribution and the sample size should be at least 30
Solution
The Central Limit Theorem (CLT) is valid when large samples are drawn from any independent and identically distributed population. So, the correct answer is option a.
Here's why:
The CLT states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).
If the population is normal, then the theorem holds true even for samples smaller than 30. Hence, it's not necessary for the population to be normally distributed (option b and d are incorrect).
Also, the samples must be independently and identically distributed. It's not enough for the samples to be just from any independent and identically distributed population (option c is incorrect).
So, the Central Limit Theorem for sampling distribution is valid only when large samples are drawn from any independent and identically distributed population.
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