Suppose that we will randomly select a pick of 64 measurements from a cosmos having a cogitate equalize to 20 and a standard deviation equal to 4. ---------------------------------------- a. amaze up the shape of the sampling diffusion of the take stiffs Ã. involuntary nervous system: Nearly normal according to the primal marge theorem. ------------------------- Do we need to make for 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 dispersal of the sample mean Ã. mean of the sample meaning = 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- shut out > 21). proffer: 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 dispersal 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 population sho! uld not be too extreme e.g. angiotensin converting enzyme 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 lack to get a dear essay, order it on our website: BestEssayCheap.com
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