X is a normally distributed random variable with a mean of 8

X is a normally distributed random variable with a mean of 8 and a standard deviation of 3.55. Find the value of X for which 92.22% of the area under the distribution curve lies to the right of it. Round your answer to 2 decimal places

Solution

Normal Distribution
Mean ( u ) = 8
Standard Deviation ( sd )=3.55
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

The value of X lies 92.22% of the area under the distribution curve lies to the right of it
                  
P ( Z > x ) = 0.9222
Value of z to the cumulative probability of 0.9222 from normal table is -1.42
P( x-u/ (s.d) > x - 8/3.55) = 0.9222
That is, ( x - 8/3.55) = -1.42
--> x = -1.42 * 3.55+8 = 2.959