Use Table A to find the proportion of observations from a st

Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.

a)  z < -0.75=

b) z > -0.75=

c)  z < 1.54=

d) -0.75 < z < 1.54=

Solution

a)
P(X < -0.75) = (-0.75-0)/1
= -0.75/1= -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.2266                  
b)
P(X > -0.75) = (-0.75-0)/1
= -0.75/1 = -0.75
= P ( Z >-0.75) From Standard Normal Table
= 0.7734                  
c)
P(X < 1.54) = (1.54-0)/1
= 1.54/1= 1.54
= P ( Z <1.54) From Standard Normal Table
= 0.9382                  
d)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -0.75) = (-0.75-0)/1
= -0.75/1 = -0.75
= P ( Z <-0.75) From Standard Normal Table
= 0.22663
P(X < 1.54) = (1.54-0)/1
= 1.54/1 = 1.54
= P ( Z <1.54) From Standard Normal Table
= 0.93822
P(-0.75 < X < 1.54) = 0.93822-0.22663 = 0.7116