LENGT OF STUDENTS COLLEGE CAREER IS NORMALLY DISTRIBUTED WIT

LENGT OF STUDENT\'S COLLEGE CAREER IS NORMALLY DISTRIBUTED WITH A MEAN LENGTH OF 5.5 YEARS AND A STANDARD DEVIATION OF 1.75 YEARS. WHAT PERCEN OF STUDENTS HAVE COLLEGE CAREERS LASTING BETWEEN 2 AND 9 YEARS?

Solution

Normal Distribution
Mean ( u ) =5.5
Standard Deviation ( sd )=1.75
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 2) = (2-5.5)/1.75
= -3.5/1.75 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 9) = (9-5.5)/1.75
= 3.5/1.75 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(2 < X < 9) = 0.97725-0.02275 = 0.9545