Find the indicated IQ score The graph depicts IQ scores of a

Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.That is, find the IQ score that separates the top 16% from the others. (Hint: Use the 68%-95% rule!) The shaded area under the curve is 16%. 130 102 115 75

Solution

Normal Distribution
Mean ( u ) =100
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.16
Value of z to the cumulative probability of 0.16 from normal table is 0.99
P( x-u/ (s.d) > x - 100/15) = 0.16
That is, ( x - 100/15) = 0.99
--> x = 0.99 * 15+100 = 114.91   ~ 115