Example 7-2: Central Limit Theorem Suppose that a random variable X has a continuous uniform distribution: 1/2, 4sx56 f(x)=D 0, otherwise Find the distribution of the sample mean of a random sample of size n = 40.

tion list estion 11 estion 12 estion 13 estion 14 estion 15 estion 16 estion 17 crunch A simple random sample of size n = 53 is obtained from a population that is skewed left with μ=77 and o=4. 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? the sample size increases. OB. Yes. 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. OC. No. 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. OD. No. 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…

2b)

rom the set of numbers {4,6, 8}, a random sample of size 2 is selected with replacement. (a) Determine the sampling distribution of the sample mean X. (b) Find the mean E(X) of the sampling distribution of the sample mean X. Compare E(X) with the population mean u.