SECTION 5.4 Sampling Distributions and the Central Limit Theorem 271 Using and Interpreting Concepts Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution. 19. Renewable Energy During a recent period of two years, the day-ahead prices for renewable energy in Germany (in euros per mega-watt hour) have a mean of 31.58 and a standard deviation of 12.293. Random samples of size 75 are drawn from this population, and the mean of each sample is determined. (Adapted from Multidisciplinary Digital Publishing Institute) 20. Renewable Energy The zloty is the official currency of Poland. During a recent period of two years, the day-ahead prices for renewable energy in Poland (in zlotys per mega-watt hour) have a mean of 158.51 and a standard deviation of 33.424. Random samples of size 100 are drawn from this population, and the mean of each sample is determined. (Adapted from Multidisciplinary Digital Publishing Institute) 21. Female Body Temperature In a recent study involving 54 women, the mean body temperature of the women was found to be 97.2°F, with a standard deviation of 0.83. Random samples of size 36 are drawn from this population, and the mean of each sample is determined. (Adapted from PLOS One) 22. Male Body Temperature In a recent study involving 42 men, the mean body temperature of the men was found to be 96.8°F, with a standard deviation of 0.61. Random samples of size 30 are drawn from this population, and the mean of each sample is determined. (Adapted from PLOS One) 23. Salaries The annual salaries for entry-level marketing analysts are normally distributed, with a mean of about $54,000 and a standard deviation of about $11,000. Random samples of 34 are drawn from this population, and the mean of each sample is determined. (Adapted from Salary.com) 24. Salaries The annual salaries for web software development managers are normally distributed, with a mean of about $136,000 and a standard deviation of about $11,500. Random samples of 40 are drawn from this population, and the mean of each sample is determined. (Adapted from Salary.com) 25. SAT French Subject Test The scores on the SAT French Subject Test for the 2018–2020 graduating classes are normally distributed, with a mean of 603 and a standard deviation of 111. Random samples of size 16 are drawn from this population, and the mean of each sample is determined. (Adapted from College Board) 26. SAT Italian Subject Test The scores on the SAT Italian Subject Test for the 2018–2020 graduating classes are normally distributed, with a mean of 628 and a standard deviation of 110. Random samples of size 25 are drawn from this population, and the mean of each sample is determined. (Adapted from College Board) 27. Repeat Exercise 25 for samples of size 40 and 60. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases? 28. Repeat Exercise 26 for samples of size 72 and 108. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases?
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