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The average income in a certain region in 2013 was $70,000 per person per year. Suppose the standard deviation is $31,000 and the distribution is right-skewed Suppose we take a random sample of 100 residents of the region. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What are the mean and standard error of the sampling distribution? c. What is the probability that the sample mean will be more than $3,100 away from the population mean? a. Choose the correct answer below. O A. Yes, it is large enough because the population standard deviation of 31,000 is larger than the sample size of 100. O B. No, it is not large enough because the sample size of 100 is less than 250. O C. No, it is not large enough because the sample size of 100 is not greater than 10% of the population. O D. Yes, it is large enough because the sample size of 100 is greater than 25. b. The mean is $ and the standard error is $ : (Type integers or decimals. Do not round.) c. The probability is. (Round to four decimal places as needed.)

The average income in a certain region in 2013 was $70,000 per person per year. Suppose the standard deviation is $31,000 and the distribution is right-skewed Suppose we take a random sample of 100 residents of the region. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What are the mean and standard error of the sampling distribution? c. What is the probability that the sample mean will be more than $3,100 away from the population mean? a. Choose the correct answer below. O A. Yes, it is large enough because the population standard deviation of 31,000 is larger than the sample size of 100. O B. No, it is not large enough because the sample size of 100 is less than 250. O C. No, it is not large enough because the sample size of 100 is not greater than 10% of the population. O D. Yes, it is large enough because the sample size of 100 is greater than 25. b. The mean is $ and the standard error is $ : (Type integers or decimals. Do not round.) c. The probability is. (Round to four decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The average income in a certain region in 2013 was $70,000 per person per year. Suppose the standard deviation is $31,000 and the distribution is right-skewed. Suppose we take a random sample of 100 residents of the region. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What are the mean and standard error of the sampling distribution? c. What is the probability that the sample mean will be more than $3,100 away from the population mean? a. Choose the correct answer below. A. Yes, it is large enough because the population standard deviation of 31,000 is larger than the sample size of 100. B. No, it is not large enough because the sample size of 100 is less than 250. C. No, it is not large enough because the sample size of 100 is not greater than 10% of the population. D. Yes, it is large enough because the sample size of 100 is greater than 25. b. The mean is $ and the standard error is $ (Type integers or decimals. Do not round.) c. The probability is (Round to four decimal places as needed.)
Transcribed Image Text:The average income in a certain region in 2013 was $70,000 per person per year. Suppose the standard deviation is $31,000 and the distribution is right-skewed. Suppose we take a random sample of 100 residents of the region. a. Is the sample size large enough to use the Central Limit Theorem for means? Explain. b. What are the mean and standard error of the sampling distribution? c. What is the probability that the sample mean will be more than $3,100 away from the population mean? a. Choose the correct answer below. A. Yes, it is large enough because the population standard deviation of 31,000 is larger than the sample size of 100. B. No, it is not large enough because the sample size of 100 is less than 250. C. No, it is not large enough because the sample size of 100 is not greater than 10% of the population. D. Yes, it is large enough because the sample size of 100 is greater than 25. b. The mean is $ and the standard error is $ (Type integers or decimals. Do not round.) c. The probability is (Round to four decimal places as needed.)
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