Determine the following areas under the standard normal z cu

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

(a) To the left of -1.27


(b) To the right of 1.27


(c) Between -1 and 2


(d) To the left of 0


(e) To the right of -4


(f) Between -1.5 and 2.5


(g) To the left of 0.23

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)
(a) To the left of -1.27
P(X < -1.27) = (-1.27-0)/1
= -1.27/1= -1.27
= P ( Z <-1.27) From Standard Normal Table
= 0.102  

(b) To the right of 1.27
P(X > 1.27) = (1.27-0)/1
= 1.27/1 = 1.27
= P ( Z >1.27) From Standard Normal Table
= 0.102

(c) Between -1 and 2
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 < 2) = (2-0)/1
= 2/1 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(-1 < X < 2) = 0.97725-0.15866 = 0.8186

(d) To the left of 0
P(X < 0) = (0-0)/1
= 0/1= 0
= P ( Z <0) From Standard Normal Table
= 0.5

(e) To the right of -4
P(X > -4) = (-4-0)/1
= -4/1 = -4
= P ( Z >-4) From Standard Normal Table
= 1

(f) Between -1.5 and 2.5
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -1.5) = (-1.5-0)/1
= -1.5/1 = -1.5
= P ( Z <-1.5) From Standard Normal Table
= 0.06681
P(X < 2.5) = (2.5-0)/1
= 2.5/1 = 2.5
= P ( Z <2.5) From Standard Normal Table
= 0.99379
P(-1.5 < X < 2.5) = 0.99379-0.06681 = 0.927  

(g) To the left of 0.23
P(X < 0.23) = (0.23-0)/1
= 0.23/1= 0.23
= P ( Z <0.23) From Standard Normal Table
= 0.591