the variable Z has a standard normal distribution find the v

the variable Z has a standard normal distribution. find the value z such that 85% of the observations fall below z

Solution

Normal Distribution
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P ( Z < x ) = 0.85
Value of z to the cumulative probability of 0.85 from normal table is 1.036
P( x-u/s.d < x - 0/1 ) = 0.85
That is, ( x - 0/1 ) = 1.04
--> x = 1.04 * 1 + 0 = 1.036