Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Related questions
Question
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.)
$
.
### Submission
To submit your answer, please click on the "Submit Answer" button below.
[Submit Answer Button]](https://content.bartleby.com/qna-images/question/62f7585f-4634-4199-81a6-58188b278fc8/0b757601-98b4-4827-b39a-3a57a746aa21/jujqu72_processed.png)
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]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 4 steps
Knowledge Booster
Similar questions
- A report announced that the median sales price of new houses sold one year was $231,000, and the mean sales price was $273,700. Assume that the standard deviation of the prices is $80,000. If you select a random sample of n=100, what is the probability that the sample mean will be betwee $275,000 and $285,000? round to four decimal placesarrow_forwardThe mean value of land and buildings per acre from a sample of farms is $1400, with a standard deviation of $300. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1169 $2285 $1490 $466 $1948 $926 ... Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply. O A. $1169 B. $1490 O C. $466 D. $1948 E. $2285 F. $926arrow_forwardThe annual income of residence in certain county is normally distributed with a mean of $42,000 and a standard deviation of $10,000. What is the probability that a randomly chosen resident has income over $52,000? 68%16%32%50%arrow_forward
- Business Weekly conducted a survey of graduates from several top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $124,000. Assume the standard deviation is $42,000. Suppose you take a simple random sample of 17 graduates. Round all answers to four decimal places if necessary What is the standard deviation of ¯¯¯XX¯? For a single randomly selected graduate, find the probability that her salary is between $111,920 and $125,213. For a simple random sample of 17 graduates, find the probability that the average salary is between $111,920 and $125,213.arrow_forwardBody temperature. Suppose the body temperature of healthy individuals is approximately normally distributed with a mean of 37.0°C and a standard deviation of 0.4°C. a. If 130 healthy individuals are randomly selected, what is the probability that the average temperature for these individuals is 36.80°C or lower? b. Would you consider an average temperature of 36.80°C as unlikely to occur if the true average temperature of healthy individuals is 37.0°C?arrow_forwardPlease answer the question in the photo. Thank you!arrow_forward
- The median annual cost of auto insurance is $ 939 (According to DACO). Suppose the standard deviation is o = $ 241. What is the probability that in a simple random sample of auto insurance policies the sample mean differs more than $ 70.42 from the population mean if the sample size is 45? You must calculate the probability that the difference between the average cost in the sample and the average annual cost do not differ by $ 70.42. Find the probability that P (\ µ - š | 0) = P (-70.42 H-iS 70.42) Select one: a. The probability is 99% that the auto policy will not differ by $ 70.42 from the average annual cost. b. The probability is 50% that the auto policy will not differ by $ 70.42 from the average annual cost. c. The probability is 80% that the auto policy will not differ by $ 70.42 from the average annual cost. d. The probability is 70% that the auto policy will not differ by $ 70.42 from the average annual cost. e. The probability is 95% that the auto policy will not differ by $…arrow_forwardIn a recent study, the Centers for Disease Control and Prevention reported that the diastolic blood pressures of adult men in the United States are normally distributed with a mean of 80.5 and standard deviation of 9.9. If an adult male is selected at random, what is the probability his diastolic blood pressure is above 90? Question 2 options: 0.1782 0.8218 0.1686 0.8314arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,