Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 6. (a) What are the mean and standard deviation of the sampling distribution of x?? ?_x? = ?_x? = Describe the shape of the sampling distribution of x?. Since n is greater than or equal to 30 the distribution of x? will be approximately normal. Since n is less than 30 the distribution of x? will be approximately normal. Since n is less than 30 we can't say what the shape of the distribution of x? will be. Since n is greater than or equal to 30 we can't say what the shape of the distribution of x? will be. (b) What is the approximate probability that x? will be within 0.2 of the population mean ?? (Round your answer to four decimal places.) (c) What is the approximate probability that x? will differ from ? by more than 0.8? (Round your answer to four decimal places.) You may need to use the appropriate table in the appendix or technology to answer this question.
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Step 1: Calculate the mean of the sampling distribution of X: Given that the population mean (μ) is 50, the mean of the sampling distribution of X will also be 50. Show more…
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Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 6. (a) What are the mean and standard deviation of the sampling distribution of x? μx = σx = Describe the shape of the sampling distribution of x. Since n is less than 30 the distribution of x will be approximately normal. Since n is greater than or equal to 30 the distribution of x will be approximately normal. Since n is less than 30 we can't say what the shape of the distribution of x will be. Since n is greater than or equal to 30 we can't say what the shape of the distribution of x will be. (b)What is the approximate probability that x will be within 0.4 of the population mean μ? (Round your answer to four decimal places.) (c)What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)
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Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 6. (a) What are the mean and standard deviation of the sampling distribution of x? μx = 50 σx = 6/√100 = 0.6 Describe the shape of the sampling distribution of x. a. Since n is less than 30, the distribution of x will be approximately normal. b. Since n is greater than or equal to 30, the distribution of x will be approximately normal. c. Since n is less than 30, we can't say what the shape of the distribution of x will be. d. Since n is greater than or equal to 30, we can't say what the shape of the distribution of x will be. (b) What is the approximate probability that x will be within 0.4 of the population mean μ? (Round your answer to four decimal places.) (c) What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)
Shaiju T.
Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p̂. Choose the phrase that best describes the shape of the sampling distribution below. Approximately normal because n ≤ 0.05N and np(1 - p) < 10. Approximately normal because n ≤ 0.05N and np(1 - p) ≥ 10. Not normal because n ≤ 0.05N and np(1 - p) < 10. Not normal because n ≤ 0.05N and np(1 - p) ≥ 10. Determine the mean of the sampling distribution of p̂. μ_p̂ = 0.4 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p̂. σ_p̂ = 0.034641 (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 88 or more individuals with the characteristic? That is, what is P(p̂ ≥ 0.44)? P(p̂ ≥ 0.44) = (Round to four decimal places as needed.)
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