Which of the following statements about the sampling distribution of the mean [distribution of sample means] and the central limit theorem [CLTlI are two? Select four {4} true statements from the list below: D - The sampling distribution is still assumed to be approximately normal if the underlying population is bimodal even if the sample size is small. D - The shape of the sampling distribution is closer to the population shape as the sample size increases. D - The sampling distribution will be approximately normal even if the population is not normal as long as the sample size is large. 0' D - pi: = p. and ": = for the sampling distribution of the mean whether or H- not the population is normal. D - From the same population. the standard error of the sampling distribution with n. = 15 will be equal to the standard error with n. = 32. D - The smaller the sample size. the smaller the standard error. CI - The smaller the sample size. the smaller the difference between the mean of the sampling distribution and the population mean. D - From the same population. the mean of the sampling distribution {pg} with n. = 'l will be equal to the mean with n. = 20. D - If the population is normally distributed. then sample size does not matter for the central limit theorem to apply. D - The sampling distribution of the mean will be approximately normal when i is large. D - If a population is perfectly normal. then for the distribution of sample means of any size. p: = p. and cr: = or. Which of the following statements are true if z is the standard normal variable? Hint: Sketch a normal curve. Select four {4} true statements from the list below: [1- Its: 3:- [1. then Pl: E o}-=:1 [1.5 [1- PT: 3 1.5) = Pf: :1 1.5] D - about 95% of the area under the normal curve lies between 3 = 2 and z = D. D - If the means of two per'l'ectlyr normal distributions are equal. their medians could be different. [1- P{z E 2] is smaller than PE: 1: 1} D- lfa 1 b. then P-[z E o} P{z E It) cannot be positive. D - The standard normal distribution has a mean of [l and a variance of 1. D- P{z E U} is smallerthan P[z 3 [l] D- P{1.5 E: z 1: 1.5] is twice PU] E z 11'. 1.5] D - The zscore corresponding to the 2?th percentile is negative