7 AbcdSolutiona PX 18 18306 1206 2 P Z a or X b P X

Solution

a)
P(X < 1.8) = (1.8-3)/0.6
= -1.2/0.6= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228                  
b)
To find P( X > a or X < b ) = P ( X > a ) + P( X < b)
P(X < 1.4) = (1.4-3)/0.6
= -1.6/0.6= -2.6667
= P ( Z <-2.6667) From Standard Normal Table
= 0.0038
P(X > 3.6) = (3.6-3)/0.6
= 0.6/0.6 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587
P( X < 1.4 OR X > 3.6) = 0.0038+0.1587 = 0.162486                  
c)
P ( Z < x ) = 0.29
Value of z to the cumulative probability of 0.29 from normal table is -0.553
P( x-u/s.d < x - 3/0.6 ) = 0.29
That is, ( x - 3/0.6 ) = -0.55
--> x = -0.55 * 0.6 + 3 = 2.6682