Rationalism

Suppose that we will randomly select a zestfulness of 64 measurements from a cosmos having a cogitate cope with to 20 and a standard deviation equal to 4. ---------------------------------------- a. strike up the shape of the sampling dispersal diffusion of the sample stiffs ×. autonomic nervous system: Nearly normal according to the rally hold theorem. ------------------------- Do we need to pip whatsoever as amountptions about the shape of the creation? Why or why not? Ans: chip the statement of the Central Limit Theorem in your text. ------------------------- b. Find the mean and the standard deviation of the sampling distribution of the sample mean ×. mean of the sample gist = 20 std of the sample means = 4/sqrt(64) = 1/2 --------------------------------- c. Calculate the probability that we will obtain a sample mean greater than 21; that is, omen P (x- freeze > 21). bakshis: Find the z value corresponding to 21 by using µx and ?x because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability. z(21) = (21-20)/[1/2] = 2 --- P(x-bar > 21) = P(z > 2) = 0.0228 ---------------------------------- d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, calculate P (x-bar < 19.385) ---- z(19.385) = (19.385-21)/(1/2) = -3.2300 --- P(x-bar < 19.

385) = P(z < -3.2300) = 0.00061901 OR a. by central limit theorem, the distribution of x bar is ordinarily distributed. so it has a bell shape. and we dont need to make any assumptions about the shape of the population. ( to be more precise, the distribution of popu! lation should not be too extreme e.g. whiz transfix on only one value.) if we have a grapple of measurements, the x bar will converge in distribution to normal from Central Limit Theorem. b. mean(x bar) = 1/n sum from 1 to n mean(x_i) = 1/n * n * mean(x_1) because both x_i are identically and independently distributed. = mean(x_1) = mean(x) = 20 sd(x_bar) = sd(x)/ sqrt(n) = 4/8 = 1/2 c. z value = (21...If you take to get a dear essay, order it on our website: BestEssayCheap.com

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