According the graph above answer the following questions bel

According the graph above answer the following questions bellow

a. What is the area under the standard normal curve to the right of z - .97?

b. What is the area under the standard normal curve to the left of z = 2.91?

c. What is the area under the standard normal curve between z = 2.53 and z = 3.09?

d. What is the area under the standard normal curve between z = -2.14 and z = -1.95?

e. What is the area under the standard normal curve to the left of z = -2.84?

f. What is the area under the standard normal curve to the right of z = -1.74?

g. If z is the standard normal variable, find P (-2.19 < z < 2.14)

h.  If z is the standard normal variable, find P (z < -1.21)

Solution

a)
P(X > -0.97) = (-0.97-0)/1
= -0.97/1 = -0.97
= P ( Z >-0.97) From Standard Normal Table
= 0.834                  
              
b)
P(X < 2.91) = (2.91-0)/1
= 2.91/1= 2.91
= P ( Z <2.91) From Standard Normal Table
= 0.9982                  

c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 2.53) = (2.53-0)/1
= 2.53/1 = 2.53
= P ( Z <2.53) From Standard Normal Table
= 0.9943
P(X < 3.09) = (3.09-0)/1
= 3.09/1 = 3.09
= P ( Z <3.09) From Standard Normal Table
= 0.999
P(2.53 < X < 3.09) = 0.999-0.9943 = 0.0047                  

d)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -2.14) = (-2.14-0)/1
= -2.14/1 = -2.14
= P ( Z <-2.14) From Standard Normal Table
= 0.01618
P(X < -1.95) = (-1.95-0)/1
= -1.95/1 = -1.95
= P ( Z <-1.95) From Standard Normal Table
= 0.02559
P(-2.14 < X < -1.95) = 0.02559-0.01618 = 0.0094                  

e)
P(X < -2.84) = (-2.84-0)/1
= -2.84/1= -2.84
= P ( Z <-2.84) From Standard Normal Table
= 0.0023                  
f)
P(X > -1.74) = (-1.74-0)/1
= -1.74/1 = -1.74
= P ( Z >-1.74) From Standard Normal Table
= 0.9591