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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 is the probability mass function of the number of successful surgeries, x? Assume the surgeries are independent.

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Answer:

An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273?279) ?Arthroscopic meniscal repair with an absorbable screw: results and surgical technique? showed that only 25 out of 37 tears (67.6%) located between 3 and 6 mm from the meniscus rim were healed.

(a) Calculate a 95% two-sided confidence interval on the proportion of such tears that will heal. Round the answers to 3 decimal places.

Step-by-step explanation:

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Answer:

PMF(X= 0,1,2)= (0.033, 0.364, 0.603)

Step-by-step explanation:

For left knee:

success(Sl)> 0.9

failure(Fl) < 0.1

for right knee:

success(Sr)= 0.67

failure(Fr)= 0.33

PMF of successful surgeries is shown in the table in the attachement :

Let X represent the number of successful surgeries: X=0, 1, 2

P(X=1) = P(Sl and Fr)+ P(Fl+ Sr) = 0.9 × 0.33 + 0.1 × 0.67= 0.364

P(X=2)= P(Sl and Sr)= 0.9 × 0.67= 0.603

P(X=0) = P(Fl anf Fr)= 0.1 × 0.33 = 0.033

PMF(X= 0,1,2)= (0.033, 0.364, 0.603)

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