In a survey conducted by a business-advisory firm of 4980 adults 18 years old and older in June 2009, during the "Great Recession," the following question was asked: How long do you think it will take to recover your personal net worth? The results of the survey follow. (Round your answers to three decimal places.) Answer (years) Respondents 1-2 3-4 5-10 ≥10 1006 1306 2119 549 (a) Determine the empirical probability distribution associated with these data. 1-2 Answer (years) Probability 3-4 5-10 210 (b) If a person who participated in the survey is selected at random, what is the probability that he or she expects that it will take 5 or more years to recover his or her personal net worth?
In a survey conducted by a business-advisory firm of 4980 adults 18 years old and older in June 2009, during the "Great Recession," the following question was asked: How long do you think it will take to recover your personal net worth? The results of the survey follow. (Round your answers to three decimal places.) Answer (years) Respondents 1-2 3-4 5-10 ≥10 1006 1306 2119 549 (a) Determine the empirical probability distribution associated with these data. 1-2 Answer (years) Probability 3-4 5-10 210 (b) If a person who participated in the survey is selected at random, what is the probability that he or she expects that it will take 5 or more years to recover his or her personal net worth?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Survey on Recovery of Personal Net Worth Post "Great Recession"**
In a survey conducted by a business-advisory firm of 4980 adults aged 18 years and older in June 2009 during the "Great Recession," the following question was asked:
**How long do you think it will take to recover your personal net worth?**
The results of the survey are shown below. (All answers are rounded to three decimal places.)
**Survey Results:**
- **Answer (years):** 1–2 | 3–4 | 5–10 | ≥ 10
- **Respondents:** 1006 | 1306 | 2119 | 549
**(a) Determine the empirical probability distribution associated with these data.**
To find the empirical probability, we need to calculate the probability for each group by dividing the number of respondents in each time range by the total number of respondents.
**Answer (years):** 1–2 | 3–4 | 5–10 | ≥ 10
- Probability: ______ | ______ | ______ | ______
**(b) Probability Calculation:**
- What is the probability that it will take 5 or more years to recover personal net worth if a person who participated in the survey is selected at random?
To answer part (b), we need to sum the probabilities of the categories "5–10" and "≥ 10."
**Explanation of Steps to Calculate Probabilities:**
1. **Calculate the total number of respondents:**
\[
1006 + 1306 + 2119 + 549 = 4980
\]
2. **Calculate individual probabilities:**
- Probability for 1–2 years:
\[
\frac{1006}{4980} \approx 0.202
\]
- Probability for 3–4 years:
\[
\frac{1306}{4980} \approx 0.262
\]
- Probability for 5–10 years:
\[
\frac{2119}{4980} \approx 0.425
\]
- Probability for ≥ 10 years:
\[
\frac{549}{4980} \approx 0.110
\]
3. **Sum the probabilities for 5–10 years and ≥ 10 years:**
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e1b5fc2-7275-49e6-a434-e3b12d2d745f%2Fbf480a7e-4807-4b7b-bcee-97dde4817312%2F89s3ovt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Survey on Recovery of Personal Net Worth Post "Great Recession"**
In a survey conducted by a business-advisory firm of 4980 adults aged 18 years and older in June 2009 during the "Great Recession," the following question was asked:
**How long do you think it will take to recover your personal net worth?**
The results of the survey are shown below. (All answers are rounded to three decimal places.)
**Survey Results:**
- **Answer (years):** 1–2 | 3–4 | 5–10 | ≥ 10
- **Respondents:** 1006 | 1306 | 2119 | 549
**(a) Determine the empirical probability distribution associated with these data.**
To find the empirical probability, we need to calculate the probability for each group by dividing the number of respondents in each time range by the total number of respondents.
**Answer (years):** 1–2 | 3–4 | 5–10 | ≥ 10
- Probability: ______ | ______ | ______ | ______
**(b) Probability Calculation:**
- What is the probability that it will take 5 or more years to recover personal net worth if a person who participated in the survey is selected at random?
To answer part (b), we need to sum the probabilities of the categories "5–10" and "≥ 10."
**Explanation of Steps to Calculate Probabilities:**
1. **Calculate the total number of respondents:**
\[
1006 + 1306 + 2119 + 549 = 4980
\]
2. **Calculate individual probabilities:**
- Probability for 1–2 years:
\[
\frac{1006}{4980} \approx 0.202
\]
- Probability for 3–4 years:
\[
\frac{1306}{4980} \approx 0.262
\]
- Probability for 5–10 years:
\[
\frac{2119}{4980} \approx 0.425
\]
- Probability for ≥ 10 years:
\[
\frac{549}{4980} \approx 0.110
\]
3. **Sum the probabilities for 5–10 years and ≥ 10 years:**
\[
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