A simple random sample of size n = 58 is obtained from a population with = 30 an

Question

A simple random sample of size n = 58 is obtained from a population with = 30 and -6. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? 0 A. 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 x become approximately normal as the sample size, n, increases. No because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n B. ° C. O D.

Explanation / Answer

B.No, the central limit theorem states that regardless of the shape of the underlying distribution the sampling distribution of X bar is approximately normal as n increases.

C.The sampling distribution of X bar is normal or approximately normal with mean =30 and standard deviation =6/root over 58=0.79

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