Question

Item19

Item19

Item 19

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

Let X denotes the completion time of procedure by method A.

X ~ Normal(31, 2²)

Let Y denotes the completion time of procedure by method B.

Y ~ Normal(35, 1²)

a) The probability that the procedure must be completed within 30 minutes by method A

The probability that the procedure must be completed within 30 minutes by method B

Since probability is higher for method A,

ans-> Method A

b) The probability that the procedure must be completed within 38 minutes by method A

The probability that the procedure must be completed within 38 minutes by method B

ans-> Method A

c) The probability that the procedure must be completed within 37 minutes by method A

The probability that the procedure must be completed within 37 minutes by method B

ans-> Method A