True or False 1. The Central Limit Theorem holds for any distribution so long as n is sufficiently large.
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True or False
1. The Central Limit Theorem holds for any distribution so long as n is sufficiently large.
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- Determine the cumulative distribution function for the uniform distribution.Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious problem in hemlock trees. Researchers have developed the following function that estimates the probability P that a given hemlock tree has ring shake: P(A,B,D)=11+e3.680.016A0.77B0.12D where A is the age of the tree yr, B is 1 if bird pecking is present and 0 otherwise, and D is the diameter in. of the tree at breast height. Source: Forest Products Journal. a. Estimate the probability that a 150-year-old tree with bird pecking present and a breast height diameter of 20in., will have ring shake. b. Estimate the probability that a 150-year-old tree, with no presence of bird pecking and a breast height diameter of 20in., will have ring shake. c. Develop a statement about what can be said about the influence have on the probability of ring shake. d. Using the total differential, estimate the probability if the actual age of the tree was 160 years and the diameter at breast height was 25in., Assume that no bird pecking was present. Compare your answer to the actual value. Hint: Assume that B=0 and exclude that variable from your calculations e. Comment on the practicality of using differentials in part d.Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.
- Example . Let the random variable X of the continuous type have the p.d.f. Ax)= 2/x, 1(True/False) The central limit theorem implies that: a All variables have bell-shaped sample data distributions if a random sample contains at least 30 observations. b Population distributions are normal whenever the population size is large. c For large random samples, the sampling distribution of y ̄ is approximately normal, regardless of the shape of the population distribution. d The sampling distribution looks more like the population distribution as the sample size increases.A recent study reported that 51% of the children in a particular community were overweight or obese. Suppose a random sample of 400 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overweight/obese children in the sample will be greater than 0.47. Complete parts (a) and (b) below. a. Before doing any calculations, determine whether this probability is greater than 50% or less than 50%. Why? O A. The answer should be greater than 50%, because 0.47 is less than the population proportion of 0.51 and because the sampling distribution is approximately Normal. O B. The answer should be less than 50%, because 0.47 is less than the population proportion of 0.51 and because the sampling distribution is approximately Normal. O C. The answer should be greater than 50%, because the resulting z-score will be positive and…Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]? (d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy basketball budget? (e) Golden State Warriors won the 2022 NBA finals. Their estimated 2022 payroll is about $194 million. Would your 2023 fantasy basketball budget be on average larger than Golden State Warriors' 2022 payroll? Explain briefly.The central limit theorem tells us (select all that apply ) - that the population of a sample means an be regarded as normal no matter what the sample size is - that as long as the sample size is greater than 30, the parent population can be assumed about normal -that as long as the sample size is greater than 30, the distribution of the sample means is about normal -that no matter what the parent population looks like the distribution of the sample means can be assumed to be normalFor any sample of size 120 the population mean, the mean of the sampling distribution for the sample means, and the sample mean will always be equal to each other. True or False When using the central limit theroem for means with n = 68, it is not necessary to assume the distribution of the population data is normally distributed. True or False The symbole op represents the standardAssume that X has the distribution N (10, 4), find: P (Z > - 3) P (11.36 < X < 16)If X has a uniform distribution on the interval from 0 to 10, then what is P(X + 7) ? IVO Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]?SEE MORE QUESTIONS
