Question

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 32 minutes and a standard deviation of 4 minutes, while method B has a mean of 36 minutes and a standard deviation of 2.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 34 minutes?

• Method A

• Method B

• Either Method

(b) Which procedure is preferred if the procedure must be completed within 42.0 minutes?

• Method A

• Method B

• Either Method

(c) Which procedure is preferred if the procedure must be completed within 40 minutes?

• Method A

• Method B

• Either Method

Answer 1

Ans:

a)

z score for Method A=(34-32)/4=0.5,Probability of completion=P(z<0.5)=0.6915

z score for Method B=(34-36)/2=-1,Probability of completion=P(z<-1)=0.1587

Method A should be preferred.

(as probability of completion within 34 minutes is higher for method A)

b)

z score for Method A=(42-32)/4=2.5,Probability of completion=P(z<2.5)=0.9938

z score for Method B=(42-36)/2=3,Probability of completion=P(z<3)=0.9987

Method B should be preferred.

c)

z score for Method A=(40-32)/4=2,Probability of completion=P(z<2)=0.9772

z score for Method B=(40-36)/2=2,Probability of completion=P(z<2)=0.9772

Either method