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a. bring up the shape of the sampling diffusion of the sample stiffs ×.
autonomic nervous system: Nearly normal according to the Central Limit theorem.
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Do we need to make 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.
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b. Find the mean and the standard deviation of the sampling distribution of the sample mean ×.
mean of the sample means = 20
std of the sample means = 4/sqrt(64) = 1/2
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c. Calculate the probability that we will obtain a sample mean greater than 21; that is, omen P (x-bar > 21). Hint: 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
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P(x-bar > 21) = P(z > 2) = 0.0228
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d. Calculate the probability that we will obtain a sample mean less than 19.385; that is,
calculate P (x-bar < 19.385)
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z(19.385) = (19.385-21)/(1/2) = -3.2300
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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 should not be too extreme e.g. one 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 want to get a dear essay, order it on our website: Orderessay
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