According the graph above answer the following questions bellow a. What is the a

Question

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)

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)

Explanation / Answer

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                  

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