The mean price of houses in a certain neighborhood is 50000

The mean price of houses in a certain neighborhood is $50,000, and the standard deviation is $10,000. Find the price range for which at least 75% of the house will sell.

Solution

Normal Distribution
Mean ( u ) =50000
Standard Deviation ( sd )=1000
Normal Distribution = Z= X- u / sd ~ N(0,1)  

P ( Z > x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is -0.67
P( x-u/ (s.d) > x - 50000/1000) = 0.75
That is, ( x - 50000/1000) = -0.67
--> x = -0.67 * 1000+50000 = $49326