Question

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 31 minutes and a standard deviation of 2 minutes, while method B has a mean of 35 minutes and a standard deviation of 1.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 30 minutes? Method A Method B Either Method

(b) Which procedure is preferred if the procedure must be completed within 38.0 minutes? Either Method Method A Method B

(c) Which procedure is preferred if the procedure must be completed within 37 minutes? Method B Either Method Method A

Answer 1

(a)

Using Method A,

The values within which 99.7% of the values lie is : 31-3*2 = 25 and 31+3*2 = 37

Using Method B,

The values within which 99.7% of the values lie is : 35-3*1 = 32 and 35+3*1 = 38

Since, 30 lies below the lower limit of Method B possible values, we choose Method A.

Correct option : Method A

(b)

Since, both the Methods have upper limit less than equal to 38 , we can choose either methods.

Correct option : Either Method

(c)

Since, upper limit of Method B is more than 37, we choose Method A

Correct option : Method A