Determine the distribution of X for the following Let X1, X2, ..., X6 be a random sample from X(10)
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- BhuroSuppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random variables with parameters α = 4,λ = 3. Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.A population has a standard deviation of 34. We take a random sample of size 30 from this population. Let Xbar be the sample mean and let Xtot be the sample sum of our sample. These are random variables.a) What is the variance of this population? b) What is the variance of Xtot? (to three decimal places) c) What is the standard deviation of Xtot? (to three decimal places) d) What is the variance of Xbar? (to three decimal places) e) What is the standard deviation of Xbar? (to three decimal places) f) What is the smallest sample size, n, which will make the standard deviation of Xtot at least 900? g) What is the smallest size sample, n, which will make the variance of Xtot at least 90000
- The central limit theorem describes three important properties of all distributions of sample means of any given sample size. What are the three properties it describes?A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or non-defective. Let X, 0 if the chip is non-defective and X; = 1 if the chip is defective. The sample fraction defective is X, +X, +---+ X, 100 What is the sampling distribution of the random variable "P?Draw all possible samples each of size n-3 from the population 2, 11 by using mpling with replacement. Find standard error of sampling distribution of &
- From a population of 4 students, a random variable (X) is measured in terms of age and the values of X are 24, 20, 22, 18. Find the sampling distribution where n = 1 Compute for the Variance when n=1The weights of all the turkeys sold in Fairfax County in 2020 were recorded in the data set “Fairfax Turkey Weights” found in the table with the column labeled "Weight". The weights are presented in pounds. There are 235,428 turkeys in this population. Does the mean calculated in the table with the column labeled "Sample (Weight)" come from a sampling distribution that is approximately Normal? Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question.Let x1, x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 75 lbs and variance 1 lb2. Let x be the sample mean weight (n = 100). (a) Describe the sampling distribution of x. The distribution is approximately normal with a mean of 75 lbs and variance of 1 lb2.The distribution is approximately normal with a mean of 75 lbs and variance of 0.01 lbs2. The distribution is unknown with a mean of 75 lbs and variance of 0.01 lbs2.The distribution is unknown with a mean of 75 lbs and variance of 1 lb2.The distribution is unknown with unknown mean and variance. (b) What is the probability that the sample mean is between 74.65 lbs and 75.35 lbs? (Round your answer to four decimal places.) P(74.65 ≤ x ≤ 75.35) = (c) What is the probability that the sample mean is greater than 75 lbs?
