Question

3) The grade point averages of a large population of college studenta is approximately normally distributed with mean 2.4 and standard deviation 0.8. What fruction of the students will possess a grade point average in excess of 3.0? 4) Refer to problem 3). If students possessing a grade point average lees than 1.9 are dropped from the college, what percentage of the students will be dropped?

Answer 1

3.

X follows a Normal distribution with mean = 2.4 and S.D = 0.8 Then z=(x-mean)/SD = (x-2.4)/0.8 follows standard Normal.

When x=3, z=(3-2.4)/0.8 = 0.75 P(Z<0.75)=0.7734 [using Normal table or Excel : NORM.S.DIST(0.75, TRUE)] P(X> 3) = 1-PCX < 3) = 1-P(Z < 0.75 ) = 1-0.7734 = 0.2266

Ans : 0.2266 or 22.66 %

4.

When x=1.9, z=(1.9-2.4)/0.8 = -0.63 P(Z<-0.63) =0.2643 [using Normal table or Excel : NORM.S.DIST(-0.63, TRUE)] P(X < 1.9) = P(Z <-0.63 ) = 0.2643

Ans : 26.43 %