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The following table shows the distribution of household incomes in 2010 for a sample of 1,000 households in a country with incomes up to $100,000. A. Compute the expected value ? and the standard deviation ? of the associated random variable X. (Round your answers to the nearest $1,000.) ?= $ ?= $

The following table shows the distribution of household incomes in 2010 for a sample of 1,000 households in a country with incomes up to $100,000. A. Compute the expected value ? and the standard deviation ? of the associated random variable X. (Round your answers to the nearest $1,000.) ?= $ ?= $

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following table shows the distribution of household incomes in 2010 for a sample of 1,000 households in a country with incomes up to $100,000.

A. Compute the expected value ? and the standard deviation ? of the associated random variable X. (Round your answers to the nearest $1,000.)

?= $
?= $
 
B. If we define a "lower-income" family as one whose income is more than one standard deviation below the mean and a "higher-income" family as one whose income is at least one standard deviation above the mean, what is the income gap between higher- and lower-income families in the country? (Round your answer to the nearest $1,000.)

$

 

### Distribution of Household Incomes (2010) The table below presents the distribution of household incomes in 2010 for a sample of 1,000 households in a country with household incomes up to $100,000. #### Income Distribution Table | Income ($1,000) | 10 | 30 | 50 | 70 | 90 | |----------------|------|------|------|------|------| | Households | 220 | 290 | 180 | 160 | 150 | ### Required Calculations 1. **Compute the expected value (µ) and the standard deviation (σ) of the associated random variable X.** - Answers should be rounded to the nearest $1,000. - \( \mu = \$ \) - \( \sigma = \$ \) 2. **Income Gap Between Lower-Income and Higher-Income Families:** - Define a "lower-income" family as one whose income is more than one standard deviation below the mean. - Define a "higher-income" family as one whose income is at least one standard deviation above the mean. - Determine the income gap between higher- and lower-income families in the country. - Round your answer to the nearest $1,000. - $<input box for the answer> ### Assistance Need help? You can find further reading materials [here](link). ### Submission To submit your answer, please click on the "Submit Answer" button below. [Submit Answer Button]
Transcribed Image Text:### Distribution of Household Incomes (2010) The table below presents the distribution of household incomes in 2010 for a sample of 1,000 households in a country with household incomes up to $100,000. #### Income Distribution Table | Income ($1,000) | 10 | 30 | 50 | 70 | 90 | |----------------|------|------|------|------|------| | Households | 220 | 290 | 180 | 160 | 150 | ### Required Calculations 1. **Compute the expected value (µ) and the standard deviation (σ) of the associated random variable X.** - Answers should be rounded to the nearest $1,000. - \( \mu = \$ \) - \( \sigma = \$ \) 2. **Income Gap Between Lower-Income and Higher-Income Families:** - Define a "lower-income" family as one whose income is more than one standard deviation below the mean. - Define a "higher-income" family as one whose income is at least one standard deviation above the mean. - Determine the income gap between higher- and lower-income families in the country. - Round your answer to the nearest $1,000. - $<input box for the answer> ### Assistance Need help? You can find further reading materials [here](link). ### Submission To submit your answer, please click on the "Submit Answer" button below. [Submit Answer Button]
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