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?

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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:**
   \[
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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