Let Z be a standard normal random variable Find the followin

Let Z be a standard normal random variable. Find the following:
Show your work!
(a) P(Z >1.03)
(b) P(1.54 <Z <2.26)
(c) k such that P (-k <Z<k)=.85

(d) k such that P(Z>k)= .04

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 1.03) = (1.03-0)/1
= 1.03/1 = 1.03
= P ( Z >1.03) From Standard Normal Table
= 0.1515                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1.54) = (1.54-0)/1
= 1.54/1 = 1.54
= P ( Z <1.54) From Standard Normal Table
= 0.93822
P(X < 2.26) = (2.26-0)/1
= 2.26/1 = 2.26
= P ( Z <2.26) From Standard Normal Table
= 0.98809
P(1.54 < X < 2.26) = 0.98809-0.93822 = 0.0499                  
d)
P ( Z > x ) = 0.04
Value of z to the cumulative probability of 0.04 from normal table is 1.75
P( x-u/ (s.d) > x - 0/1) = 0.04
That is, ( x - 0/1) = 1.75
--> x = 1.75 * 1+0 = 1.751