Suppose a simple random sample of size n = 49 is obtained from a population with ? = 82 and ? = 28. (a) Describe the sampling distribution of x?. (b) What is P (x? > 89)? (c) What is P (x? ? 73.2)? (d) What is P (77 < x? < 90.8)? (a) Choose the correct description of the shape of the sampling distribution of x?. A. The distribution is uniform. B. The distribution is skewed right. C. The distribution is approximately normal. D. The distribution is skewed left. E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of x?. ?_x? = 81 ?_x? = 4 (b) P (x? > 89) = .0228 (Round to four decimal places as needed.) (c) P (x? ? 73.2) = [ ] (Round to four decimal places as needed.) (d) P (77 < x? < 90.8) = [ ] (Round to four decimal places as needed.)
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It should be a population with mean μ = 82 and standard deviation σ = 28. (a) Since the sample size n = 49 is large enough (n > 30), we can say that the sampling distribution of the sample mean (x̄) is approximately normal due to the Central Limit Theorem. The Show more…
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