1. Based on the data investigated in an article within the field of surgical pro
ID: 2935486 • Letter: 1
Question
1. Based on the data investigated in an article within the field of surgical procedures, anterior cruciate ligament surgery at high-volume hospitals (with more than 300 surgeries per year) is normally distributed with a mean of 129 minutes and a standard deviation of 14 minutes.
a. What is the probability that such surgery at a high-volume hospital requires a time more than two standard deviations above the mean? (7 pts)
b. What is the probability that such surgery at a high-volume hospital is completed in less than 100 minutes? (7 pts)
c. The probability of a completed surgery at a high-volume hospital is equal to 95% at what time? (6 pts)
d. If same surgery requires 199 minutes in a different hospital, what do you conclude about the volume of such surgeries at that hospital? Explain.(10 pts)
Explanation / Answer
Mean = 129 minutes
Standard deviation = 14 minutes
A) p(time is more than 2 standard deviations above mean)
= p(Z > 2)
= 1 - P(Z < 2)
= 1 - 0.9772
= 0.0228
B) P(X < 100)
= P(Z < (100 - 129)/14)
= P(Z < -2.07)
= 0.0192
C) P(X < A) = 0.95
P(Z < (A - 129)/14) = 0.95
(A - 129)/14 = 1.645
A = 152.03 minutes
D) P(X > 199) = 1 - P(Z < (199 - 129)14)
= 1 - P(Z < 5)
= 0
The surgery takes unusually high time at this hospital.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.