Determine the following standard normal z curve areas Round

Determine the following standard normal (z) curve areas. (Round all answers to four decimal places.)

(a) The area under the z curve to the left of 1.73


(b) The area under the z curve to the left of

0.69

(c) The area under the z curve to the right of 1.3


(d) The area under the z curve to the right of

2.82

(e) The area under the z curve between 2.22 and 0.52


(f) The area under the z curve between

1

and 1


(g) The area under the z curve between

4

and 4

Solution

Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                      
(a) The area under the z curve to the left of 1.73

P(X < 1.73) = (1.73-0)/1
= 1.73/1= 1.73
= P ( Z <1.73) From Standard Normal Table
= 0.9582  

(b) The area under the z curve to the left of
-0.69

P(X < -0.69) = (-0.69-0)/1
= -0.69/1= -0.69
= P ( Z <-0.69) From Standard Normal Table
= 0.2451                  

(c) The area under the z curve to the right of 1.3

P(X > 1.3) = (1.3-0)/1
= 1.3/1 = 1.3
= P ( Z >1.3) From Standard Normal Table
= 0.0968                  

(d) The area under the z curve to the right of
-2.82

P(X > -2.82) = (-2.82-0)/1
= -2.82/1 = -2.82
= P ( Z >-2.82) From Standard Normal Table
= 0.9976                  

(e) The area under the z curve between -2.22 and 0.52
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -2.22) = (-2.22-0)/1
= -2.22/1 = -2.22
= P ( Z <-2.22) From Standard Normal Table
= 0.01321
P(X < 0.52) = (0.52-0)/1
= 0.52/1 = 0.52
= P ( Z <0.52) From Standard Normal Table
= 0.69847
P(-2.22 < X < 0.52) = 0.69847-0.01321 = 0.6853                  

(f) The area under the z curve between
-1
and 1
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -1) = (-1-0)/1
= -1/1 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 1) = (1-0)/1
= 1/1 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(-1 < X < 1) = 0.84134-0.15866 = 0.6827                  

(g) The area under the z curve between
-4
and 4
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -4) = (-4-0)/1
= -4/1 = -4
= P ( Z <-4) From Standard Normal Table
= 0.00003
P(X < 4) = (4-0)/1
= 4/1 = 4
= P ( Z <4) From Standard Normal Table
= 0.99997
P(-4 < X < 4) = 0.99997-0.00003 = 0.9999