Question

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 35 minutes and a standard deviation of 4 minutes, while method B has a mean of 39 minutes and a standard deviation of 2.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 35 minutes?

• Method A

• Method B

• Either Method

(b) Which procedure is preferred if the procedure must be completed within 45.0 minutes?

• Method A

• Method B

• Either Method

(c) Which procedure is preferred if the procedure must be completed within 43 minutes?

• Method A

• Method B

• Either Method

Answer 1

Ans:

a)

For method A:

z=(35-35)/4=0

P(z<=0)=0.50

For method B:

z=(35-39)/2

z=-2

P(z<=-2)=0.0228

Probability of completion within 35 minutes is higher for method A.So,

Method A should be preferred.

b)

For method A:

z=(45-35)/4=2.5

P(z<=2.5)=0.9938

For method B:

z=(45-39)/2

z=3

P(z<=3)=0.9987

Probability of completion within 45 minutes is higher for method B.So,

Method B should be preferred.

c)

For method A:

z=(43-35)/4=2

P(z<=2)=0.9773

For method B:

z=(43-39)/2

z=2

P(z<=3)=0.9773

Probability of completion within 43 minutes is equal for both methods.So,

Either method