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 8 minutes, while method B has a mean of 29 minutes and a standard deviation of 4.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 27 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

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

• Method A

• Method B

• Either Method

Answer 1

a)for method A:

probability =

P(X<27)

=

P(Z<0.25)=

0.5987

for method B:

probability =

P(X<27)

=

P(Z<-0.5)=

0.3085

hence Method A is preferred

b)for method A:

probability =

P(X<35)

=

P(Z<1.25)=

0.8944

for method B:

probability =

P(X<35)

=

P(Z<1.5)=

0.9332

hence Method B is preferred

c)

for method A:

probability =

P(X<33)

=

P(Z<1)=

0.8413

for method B:

probability =

P(X<33)

=

P(Z<1)=

0.8413

Either Method is preffered