Question

Homework: Q Sampling Distn... CLT Save Score: 0 of 1 pt HW Score: 18.25%, 3.83 of 21 pts 2 of 8 (8 complete) X 8.1.8 Question Help simple random sample of sizen 44 is obtained from a population with u 31 and o approximately normally distributed? Why? What is the sampling distribution of x? 6. Does the population need to be normally distributed for the sampling distribution of x to be Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? O A. 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. OB. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases C. 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 ormal as the sample size.n. increases. n 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. What is the sampling distribution of x? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.) O A. The sampling distribution of x is uniform with and a O B. The sampling distribution of x follows Student's t-distribution with and a O C. The sampling distribution of x skewed left with and o O D. The sampling distribution of x is normal or approximately normal with H and a ? Click to select and enter your answer(s) and then click Check Answer. All parts showing Clear All Check Answer

Answer 1

SOLUTION:-

What is the sampling distribution $\bar{x}$:-

Option D is correct.

$\mu _{\bar{x}}=Mean=31$

$\sigma =6$  $n=44$

$\sqrt{n}=\sqrt{44}=6.633249581$

$\sigma _{\bar{x}}=\frac{6}{6.633249581}$

$\sigma _{\bar{x}}=0.9045$