Suppose a simple random sample of size n = 36 is obtained from a population with ? = 82 and ? = 18. (a) Describe the sampling distribution of x?. (b) What is P (x? > 87.1)? (c) What is P (x? ? 75.1)? (d) What is P (80.2 < x? < 86.65)? Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Choose the correct description of the shape of the sampling distribution of x?. A. The distribution is approximately normal. B. The distribution is skewed right. C. The distribution is skewed left. D. The distribution is uniform. E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of x?. ?_x? = ?_x? = (b) P (x? > 87.1) = (Round to four decimal places as needed.) (c) P (x? ? 75.1) = (Round to four decimal places as needed.) (d) P (80.2 < x? < 86.65) = (Round to four decimal places as needed.)
Added by William A.
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Mean (µ) = p = 82 Standard deviation (σ) = σ_population / √n = 18 / √36 = 18 / 6 = 3 (a) Since the sample size is large (n = 36), the sampling distribution of x will be approximately normal according to the Central Limit Theorem. Now, we need to find the Show more…
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