A simple random sample of size n = 59 is obtained from a population with mu = 43

Question

A simple random sample of size n = 59 is obtained from a population with mu = 43 and sigma = 5. Does the population need to be normally distributed for the sampling distribution of bar x to be approximately normally distributed? Why? What is the sampling distribution of bar x? Does the population need to be normally distributed for the sampling distribution of bar x to be approximately normally distributed? Why? No because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of bar x becomes approximately normal as the sample size, n, increases. No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of bar x becomes approximately normal as the sample size, n, increases. No because the Central Limit Theorem states that only for underlying population that are normal is the shape of the sampling distribution of bar x normal, regardless of the sample size, n. Yes because the Central Limit Theorem states that the sampling variability populations will increases as the sample size n increases. What is the sampling distribution of bar x? Select the correct choice below and fill in the answer boxes within your choice.

Explanation / Answer

As n=59 > 31 which is generally the vutoff value for being a large n value.

Therefore by Central limit theorem, sample means will have an approximately normal distribution irrespective whether the population has a normal distribution or not.

Therefore a) is the correct answer.

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