Question

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 25 minutes and a standard deviation of 6 minutes, while method B has a mean of 29 minutes and a standard deviation of 3.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 25 minutes?

• Method A

• Method B

• Either Method

(b) Which procedure is preferred if the procedure must be completed within 35.0 minutes?

• Method A

• Method B

• Either Method

(c) Which procedure is preferred if the procedure must be completed within 33 minutes?

• Method A

• Method B

• Either Method

Answer 1

Let X denote the times for a surgical procedure. Then it is given that, the surgical procedure that can be completed using two methods, that is:

For Method A: and for Method B:

(a) To obtain which procedure is preferred if the procedure must be completed within 25 minutes, we obtain:

For Method A:

Again, for Method B:

Thus, we observe that the probability of completing the surgical procedure using Method B is higher than Method A, and hence, Method B is preferred if the procedure must be completed within 25 minutes.

(b) To obtain which procedure is preferred if the procedure must be completed within 35 minutes, we obtain:

For Method A:

Again, for Method B:

Thus, we observe that the probability of completing the surgical procedure using Method B is higher than Method A, and hence, Method B is preferred if the procedure must be completed within 35 minutes.

(c) To obtain which procedure is preferred if the procedure must be completed within 33 minutes, we obtain:

For Method A:

Again, for Method B:

Thus, we observe that the probability of completing the surgical procedure using Method B is same as Method A, and hence, either of the two Methods can be preferred if the procedure must be completed within 33 minutes.