Given a normal distribution with = 50 and =4, and given you select a sample of n=100,

a. What is the probability that X is less than 49?

A. P(X < 49) =NORM.DIST(49,50,4/SQRT(100),0) =0.0438

B. P(X < 49) =NORM.DIST(49,50,4/SQRT(100),1) =0.0062

C. P(X < 49) =NORM.DIST(49,50,4,0) =0.0967

D. P(X < 49) =NORM.DIST(49,50,4/100,1) =3.0567E-138

b. What is the probability that

X is between 49 and 51.5?

A. P(49 < X < 51.5) =NORM.DIST(51.5,50,0.4,0)-NORM.DIST(49,50,0.4,0)= -0.0429

B. P(49 < X < 51.5) =NORM.DIST(51.5,50,0,4,1)+NORM.DIST(49,50,0.4,1) =1.0061

C. P(49 < X < 51.5) =NORM.DIST(51.5,50,4,1)-NORM.DIST(49,50,4,1) =0.2449

D. P(49 < X < 51.5) =NORM.DIST(51.5,50,0.4,1)-NORM.DIST(49,50,0.4,1) =0.9937

c. What is the probability that X is above 51.5?

A. P(X > 51.5) =NORM.DIST(51.5,50,0.4,0) =0.0009

B. P(X > 51.5) =NORM.DIST(51.5,50,0.4,1) =0.9999

C. P(X > 51.5) =1-NORM.DIST(51.5,50,4,1) =0.3538

D. P(X> 51.5) =1-NORM.DIST(51.5,50,0.4,1) =8.8417E-05

d. There is a 35% chance that X is above what value?

A.For P(X> X)=0.35, use =NORM.INV(0.65,50,4) =48.46

B.For P(X > X)=0.35, use =NORM.INV(0.65,50,0.4) =50.15

C. ForP(X > X)=0.35, use =NORM.INV(0.35,50,0.4) =49.85

D. ForP(X > X)=0.35, use =1-NORM.INV(0.65,50,0.4) = -49.15