An article in Knee Surgery, Sports Traumatology, Arthroscopy, "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique," (2005, Vol. 13, pp. 273-279) cites a success rate more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate for tears of 3-6 mm. If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what are the mean and variance of the number of successful surgeries? Assume the surgeries are independent. Round your answers to three decimal places (e.g. 98.765). Mean = i Variance = i
An article in Knee Surgery, Sports Traumatology, Arthroscopy, "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique," (2005, Vol. 13, pp. 273-279) cites a success rate more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate for tears of 3-6 mm. If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what are the mean and variance of the number of successful surgeries? Assume the surgeries are independent. Round your answers to three decimal places (e.g. 98.765). Mean = i Variance = i
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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![### Example Problem: Calculating Mean and Variance of Successful Surgeries
An article in **Knee Surgery, Sports Traumatology, Arthroscopy** titled "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique" (2005, Vol. 13, pp. 273-279) cites a success rate of more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate for tears of 3-6 mm.
If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what are the mean and variance of the number of successful surgeries? Assume the surgeries are independent.
**Round your answers to three decimal places (e.g., 98.765).**
#### Inputs:
- **Mean =** [Input Box]
- **Variance =** [Input Box]
#### Explanation:
To solve this problem, the following steps should be undertaken:
1. **Identify Success Rates:**
- The success rate for a meniscal tear of less than 3 mm is **more than 90%**. For the purpose of this example, assume it to be **0.90**.
- The success rate for a meniscal tear of 3-6 mm is **0.67**.
2. **Calculate Mean and Variance for Independent Events:**
- For two surgeries, we calculate both mean and variance of the number of successful surgeries.
- Let \( X_1 \) be the success indicator for the left knee surgery and \( X_2 \) for the right knee surgery.
- \( X_1 \sim Bernoulli(p_1) \), where \( p_1 = 0.90 \)
- \( X_2 \sim Bernoulli(p_2) \), where \( p_2 = 0.67 \)
3. **Mean Calculation:**
- \( E(X_1) = p_1 = 0.90 \)
- \( E(X_2) = p_2 = 0.67 \)
- The total mean, \( E(X_1 + X_2) = E(X_1) + E(X_2) \)
- Thus, \( \text{Mean} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F844f36b2-dadc-4b67-b29f-70387e2f5e38%2F36edee02-3ebe-4aac-a8e6-5f2555508bc8%2Fe6n7tyau_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem: Calculating Mean and Variance of Successful Surgeries
An article in **Knee Surgery, Sports Traumatology, Arthroscopy** titled "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique" (2005, Vol. 13, pp. 273-279) cites a success rate of more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate for tears of 3-6 mm.
If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what are the mean and variance of the number of successful surgeries? Assume the surgeries are independent.
**Round your answers to three decimal places (e.g., 98.765).**
#### Inputs:
- **Mean =** [Input Box]
- **Variance =** [Input Box]
#### Explanation:
To solve this problem, the following steps should be undertaken:
1. **Identify Success Rates:**
- The success rate for a meniscal tear of less than 3 mm is **more than 90%**. For the purpose of this example, assume it to be **0.90**.
- The success rate for a meniscal tear of 3-6 mm is **0.67**.
2. **Calculate Mean and Variance for Independent Events:**
- For two surgeries, we calculate both mean and variance of the number of successful surgeries.
- Let \( X_1 \) be the success indicator for the left knee surgery and \( X_2 \) for the right knee surgery.
- \( X_1 \sim Bernoulli(p_1) \), where \( p_1 = 0.90 \)
- \( X_2 \sim Bernoulli(p_2) \), where \( p_2 = 0.67 \)
3. **Mean Calculation:**
- \( E(X_1) = p_1 = 0.90 \)
- \( E(X_2) = p_2 = 0.67 \)
- The total mean, \( E(X_1 + X_2) = E(X_1) + E(X_2) \)
- Thus, \( \text{Mean} =
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