Suppose that out of 10,351 convicts who escaped from U.S. prisons, only 7767 were recaptured. Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. Round your answer to four decimal places. Op=0.8735 O p = 0.0000 Op=0.2496 p=0.7504 p=1.0000
Suppose that out of 10,351 convicts who escaped from U.S. prisons, only 7767 were recaptured. Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. Round your answer to four decimal places. Op=0.8735 O p = 0.0000 Op=0.2496 p=0.7504 p=1.0000
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![**Proportion of Recaptured Convicts: Calculation Task**
**Question:**
Suppose that out of 10,351 convicts who escaped from U.S. prisons, only 7,767 were recaptured. Let \( p \) represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for \( p \). Round your answer to four decimal places.
**Choices:**
- \( \hat{p} = 0.8735 \)
- \( \hat{p} = 0.0000 \)
- \( \hat{p} = 0.2496 \)
- \( \hat{p} = 0.7504 \)
- \( \hat{p} = 1.0000 \)
**Explanation:**
To find the point estimate \( \hat{p} \) for the proportion of all escaped convicts who are eventually recaptured, you use the formula for the sample proportion:
\[ \hat{p} = \frac{x}{n} \]
where:
- \( x \) is the number of successes (recaptured convicts),
- \( n \) is the total number of trials (escaped convicts).
Given:
- Total number of escaped convicts \( n = 10,351 \),
- Number of recaptured convicts \( x = 7,767 \).
Calculate \( \hat{p} \):
\[ \hat{p} = \frac{7,767}{10,351} \approx 0.7504 \]
Therefore, the correct point estimate for \( p \), rounded to four decimal places, is 0.7504.
This calculation involves comparing the proportion given in the data with the potential options to choose the one that correctly matches the calculated result. The solution involves basic arithmetic computation and rounding to the fourth decimal place as specified.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6805edd-9acc-4ccd-9c7a-22df1558ea0b%2Fc151e424-43ad-4bf4-95cb-9b4eac96c6c4%2F5tc9on3j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Proportion of Recaptured Convicts: Calculation Task**
**Question:**
Suppose that out of 10,351 convicts who escaped from U.S. prisons, only 7,767 were recaptured. Let \( p \) represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for \( p \). Round your answer to four decimal places.
**Choices:**
- \( \hat{p} = 0.8735 \)
- \( \hat{p} = 0.0000 \)
- \( \hat{p} = 0.2496 \)
- \( \hat{p} = 0.7504 \)
- \( \hat{p} = 1.0000 \)
**Explanation:**
To find the point estimate \( \hat{p} \) for the proportion of all escaped convicts who are eventually recaptured, you use the formula for the sample proportion:
\[ \hat{p} = \frac{x}{n} \]
where:
- \( x \) is the number of successes (recaptured convicts),
- \( n \) is the total number of trials (escaped convicts).
Given:
- Total number of escaped convicts \( n = 10,351 \),
- Number of recaptured convicts \( x = 7,767 \).
Calculate \( \hat{p} \):
\[ \hat{p} = \frac{7,767}{10,351} \approx 0.7504 \]
Therefore, the correct point estimate for \( p \), rounded to four decimal places, is 0.7504.
This calculation involves comparing the proportion given in the data with the potential options to choose the one that correctly matches the calculated result. The solution involves basic arithmetic computation and rounding to the fourth decimal place as specified.
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