Assume X is normally distributed with a mean of 14 and a sta

Assume X is normally distributed with a mean of 14 and a standard deviation of 2. Determine the value for x that solves each of the following. Round the answers to 2 decimal places.

a) P(X>x)=0.5           x=?

b) P(X>x)=0.95        x=?

c) P(x<X<14)=0.2    x=?

Solution

a)
P ( Z > x ) = 0.5
Value of z to the cumulative probability of 0.5 from normal table is 0
P( x-u/ (s.d) > x - 14/2) = 0.5
That is, ( x - 14/2) = 0
--> x = 0 * 2+14 = 14                  
b)
P ( Z > x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is -1.64
P( x-u/ (s.d) > x - 14/2) = 0.95
That is, ( x - 14/2) = -1.64
--> x = -1.64 * 2+14 = 10.71