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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Concept explainers

Question

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

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

(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.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.