o N 5.4 SAMPLING DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM USING AND INTERPRET
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o N 5.4 SAMPLING DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM USING AND INTERPRETING CONCEPTS 271 Using the Central Limit Theorem In Exercises l Limit Theorem e mean and standard deviation se the Centra us, Then of the indicated sampling sketch a distribution of sample 19. graph of the sampling distribution Braking Distances The braking distances (from 60 miles per hour to a complete stop on dry pavement) of a sports utility vehicle are normally ributed, with a mean of 154 feet and a standard deviation of 5.12 feet Random samples of size are drawn from this population, and the mean of each sample is determined. (Ad er Repor 20. Braking Distances The braking distances (from 60 miles per hour to a complete stop on dry pavement) of a car are normally distributed, with a mean of 136 feet and a standard deviation of 4.66 feet. Random samples of size 15 are drawn from this population, and the mean of each sample is (Adapted from Cons determined er Reports) 21. SAT Critical Reading scores: Males The scores for males on the critical reading portion of the SAT are normally distributed, with a mean of 498 and a standard deviation of 116. Random samples of size 20 are drawn from this population, and the mean of each sample is determined. (Source: The College Boar 22. SAT Critical Reading Scores: Females The scores for females on the critical reading portion of the SAT are normally distribute with a mean of 493 and a standard deviation of 112. Random samples are drawn from this population, and the mean of each sample is determined. e College Board) 23. Canned Fruit The annual per capita consumption of canned fruit by people in the United States is normally distributed, with a mean of 10 pounds and a tandard deviation of 1.8 pounds. Random samples of size 25 are drawn from this popu on, and the mean of each sample is determined. US Department of Agriculture) consumption of canned 24. Canned vegetables The annual per capita with a distributed, vegetables by people in the United States is normally sample mean and a standard deviation of 3.2 pounds. Random of size 30 are drawn fron this popu determined. (Adapted from US Department of Agriculture) 25. Repeat Exercise for sampl es of size 24 and 36. W happens to the mean and the standard deviation of the distribution of sample means as the size of 6. Repeat Exercise 20 for samples of size 30 and 45. What happens to the mean and the standard dev the sample increases e indicated probability d the probab Finding Probabilities In use technology to the specialists annual salary for environmental compliance from is 27. The mean sample of 35 salary of the sample s about $60,000. A random that the mean $65,700 What is the probability about population. Assume than for flight attendan his popu than from less n annual salary of the sample is e mean annual salary 28. SalariesExplanation / Answer
22.
Mean =493
Standard error = 112/sqrt(36) =18.6667
25
Mean =493
For sample size 24, Standard error = 112/sqrt(24) =22.8619
For sample size 36, Standard error = 112/sqrt(36) =18.6667
Sample mean remains the same. ( or tends to population mean)
When sample size increases, the standard error decreases.
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