If the number of sample is less than 30 (n<30), what is the requirement for the population to apply the central Limit Theorem?
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If the number of sample is less than 30 (n<30), what is the requirement for the population to apply the central Limit Theorem?
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- A simple random sample of size n = 37 is obtained from a population that is skewed left with µ = 31 and o=4. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? A. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. B. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. C. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. D. Yes. The central limit theorem…Let S={1,2,3,4,5,6,7,8} be a sample space with P(x)=k^2x where x is a member of S, and k is a positive constant. Compute E(S). Round your answer to the nearest hundredths.When using the central limit theorem for means with n = 98, it is not necessary to assume the distribution of the population data is normally distributed. True False
- A simple random sample of size n= 32 is obtained from a population that is skewed left with u = 58 and o = 10. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? O A. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. O B. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size,n. O C. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. O D. No. The central limit theorem states that only if the…The Central Limit Theorem (CLT) says O Samples of size 15 are large enough for the CLT to apply for any populations. O As the sample size increases, the sampling distribution of the mean will get closer and closer to a normal distribution. O Regardless of the sample size, the sampling distribution of the mean is always close to a normal distribution. O Only for symmetric population distributions, the sampling distribution of the mean will get close to a normal distribution as the sample size increases.Suppose 10% of students are veterans. From a sample of 279 students, how unusual would it be to have less than 20 veterans?Is the success-failure condition of the Central Limit Theorem satisfied? A) No. Either np < 10 or n(1−p) < 10. B) Yes. Both np and n(1−p) are ≥10. The Central Limit Theorem tells us that the distribution of sample proportions approximately follows a _______ distribution with mean ____ and standard deviation _____ .Given this knowledge, use technology to compute the probability that, through random selection, one finds a sample proportion that is less than the proportion corresponding to 20 veterans.Round answer to 4 decimal places. Is this result unusual? A) Yes. There is a less than 5% chance of this happening by random variation. B) No. There is at least a 5% chance of this happening by random variation.
- 52. Components are manufactured via a process in which 5% of all components produced are deemed to be defective. Consider a random sample of 300 of these components and let X denote the number of defective components found in the sample: (a) Which common discrete distribution does X have (include parameter(s))? Justify your answer. (b) According to the Central Limit Theorem, what is the approximate distribution of X (include param- eter(s))? (c) Approximate P(X < 15) using the continuity correction.When using the central limit theorem for means with n = 60, it is not necessary to assume the distribution of the population data is normally distributed. True FalseGiven that (7000) fresh graduated IT students in Jordan participated in a Fortinet NSE4 exam in whichthe highest score is 100. Their results were normally distributed with an average of (70) and standarddeviation of (10). If you knew that the passing score to get certified is (85), then:a. Find the number of students who get certified.b. If (792) students were actually certified, what was the minimum score achieved?
- According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and o = 56, the mean of the sampling distribution of sample means would equal 8 100 800 80 O O o O OA simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this is the parameter value for the population. You take a simple random sample of 25 Americans and let p(hat) equal the proportion in the sample who get 30 minutes of exercise at least five days per week. Does the sampling distribution pass the Normal condition? 1) Yes because n >= 30 2) No, because n < 30 3) Cannot be determined 4) No, because np < 10 5) Yes, because n (1-p) >= 10
