The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be $3,000 per year with a standard deviation of $6,000. We randomly survey 1,000 residents of that country. (a) In words, define the random variable X. the number of people surveyedthe number of people who have a salary of $3,000 per year the yearly income of someone in a Third World countrythe yearly income for each person in a Third World country (b) In words, define the random variable X. the average salary from a sample of 1,000 residents of a Third World countrythe average salary of all residents in the world the average salary from a sample of 1,000 people throughout the worldthe average salary of all residents in a Third World country (c) Give the distribution of X. (Round your numerical values to two decimal places.) X ~ , (d) How is it possible for the standard deviation to be greater than the average? Very wide differences in data values can have averages smaller than standard deviations.Very small differences in data values can have averages smaller than standard deviations. This is an example of a poor survey; the average should never be smaller than the standard deviation. (e) Why is it more likely that the average of the 1,000 residents will be from $3,000 to $3,100 than from $3,100 to $3,200? The sample size was sufficiently large to ensure a sample mean close to the population mean.It is actually more likely that the average of the 1,000 residents will be from $3,100 to $3,200. Because the standard deviation is so high, there is a high probability the sample mean is close to the population mean.The distribution of the sample mean will have higher probabilities closer to the population mean.
The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be $3,000 per year with a standard deviation of $6,000. We randomly survey 1,000 residents of that country. (a) In words, define the random variable X. the number of people surveyedthe number of people who have a salary of $3,000 per year the yearly income of someone in a Third World countrythe yearly income for each person in a Third World country (b) In words, define the random variable X. the average salary from a sample of 1,000 residents of a Third World countrythe average salary of all residents in the world the average salary from a sample of 1,000 people throughout the worldthe average salary of all residents in a Third World country (c) Give the distribution of X. (Round your numerical values to two decimal places.) X ~ , (d) How is it possible for the standard deviation to be greater than the average? Very wide differences in data values can have averages smaller than standard deviations.Very small differences in data values can have averages smaller than standard deviations. This is an example of a poor survey; the average should never be smaller than the standard deviation. (e) Why is it more likely that the average of the 1,000 residents will be from $3,000 to $3,100 than from $3,100 to $3,200? The sample size was sufficiently large to ensure a sample mean close to the population mean.It is actually more likely that the average of the 1,000 residents will be from $3,100 to $3,200. Because the standard deviation is so high, there is a high probability the sample mean is close to the population mean.The distribution of the sample mean will have higher probabilities closer to the population mean.
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 distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be $3,000 per year with a standard deviation of $6,000. We randomly survey 1,000 residents of that country.
(a) In words, define the random variable X.
(b) In words, define the random variable
(c) Give the distribution of
,
(d) How is it possible for the standard deviation to be greater than the average?
(e) Why is it more likely that the average of the 1,000 residents will be from $3,000 to $3,100 than from $3,100 to $3,200?
the number of people surveyedthe number of people who have a salary of $3,000 per year the yearly income of someone in a Third World countrythe yearly income for each person in a Third World country
(b) In words, define the random variable
X.
the average salary from a sample of 1,000 residents of a Third World countrythe average salary of all residents in the world the average salary from a sample of 1,000 people throughout the worldthe average salary of all residents in a Third World country
(c) Give the distribution of
X.
(Round your numerical values to two decimal places.)X ~
(d) How is it possible for the standard deviation to be greater than the average?
Very wide differences in data values can have averages smaller than standard deviations.Very small differences in data values can have averages smaller than standard deviations. This is an example of a poor survey; the average should never be smaller than the standard deviation.
(e) Why is it more likely that the average of the 1,000 residents will be from $3,000 to $3,100 than from $3,100 to $3,200?
The sample size was sufficiently large to ensure a sample mean close to the population mean.It is actually more likely that the average of the 1,000 residents will be from $3,100 to $3,200. Because the standard deviation is so high, there is a high probability the sample mean is close to the population mean.The distribution of the sample mean will have higher probabilities closer to the population mean.
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