An article in Knee Surgery Sports Traumatology, Arthroscopy [“Effect of Provider Volume on Resource Utilization for Surgical Procedures” (2005, Vol. 13, pp. 273–279)] showed a mean time of 129 minutes and a standard deviation of 14 minutes for ACL reconstruction surgery for high-volume hospitals (with more than 300 such surgeries per year). If a high-volume hospital needs to schedule 10 surgeries, what are the mean and variance of the total time to complete these surgeries? Assume that the times of the surgeries are independent and normally distributed.

Step 1 of 2:

Our goal is:

We need to find the mean and variance of the total time to complete these surgeries.

Let denote the 10 surgeries time.

The total time taken for 10 surgeries is also a random variable,

T = .

We know that the mean and the variance of one surgery.

E(X) = 129 and

V(X) = 14

V(X) = 196

Now the mean of all 10 surgery is E(T).

All surgeries are independent of each other that’s why .

E(T)...