Let x be a continuous random variable that follows a normal

Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation 25.

Find the value of x so that the area under the normal curve to the right of x is 0.8023.

Solution

Normal Distribution
Mean ( u ) =200
Standard Deviation ( sd )=25
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.8023
Value of z to the cumulative probability of 0.8023 from normal table is 0.85
P( x-u/s.d < x - 200/25 ) = 0.8023
That is, ( x - 200/25 ) = 0.85
--> x = 0.85 * 25 + 200 = 221.25