Question

uiz: Chapter 7 Quiz s Question:1 pt 6 of 6 This Quiz: 6 pts pos Asimple random sample ot size n«T8isottainedfrom a population with ?.32ando.8 ampling distribution of x be normally distrieuled for the sampling distribution of x to be approximately nomally distributed? Why? What is he Does the population need to be normally distributed for the t sampling ostriution of x to be approximately normally destibuted? why No because the Central Limil Theorem states that only i the shape of the underlying population is normal or uniorm does the sampling disibution of i become approximately normal as the samplie sine, n inoreases Ceretai Unit Theorem statestat ony tor undehrg poplatons that are normal-the shape ofte samping diabbulon of x norm al, regardless ofte saple the Central Limit Thecrem states that the sampling variablity of nonnomal populations will increase as the sample size increases because ?, O C. Yes because O D. No because the Central Limit Theorem s tales that regardiess of the shape of the underlying population, the sampling distibution of i becomes approaimately nomal as the sample size, nt inoreases What is the sampling distribution of x? Select the comect choice below and tit in the answer boxes within your choice Type integers or decimals rounded to three decimal places as needed ) ?A. Tho sanping tulonofxis normal or approximately nonnal win ri". land..- G The sampling dstribution of i is skewed leth with and Click to seliect and enter your anwer 20 2 3 4 5

Answer 1

Definition of central limit theorem:

The Central Limit Theorem states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.

Answer: D) 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.

Answer: A) The sampling distribution of x? is normal or approximately normal with µ _x? = 32

and ? _x?= ?/?n = 8/?78 = 0.9058.

Therefore, if X~N(32,64) then X? ~ N(32,0.8205)