A study has shown that 17 of all college textbooks have a pr

A study has shown that 17% of all college textbooks have a price of $95 or higher. It is known that the standard deviation of the prices of all college textbooks is $9.5 . Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Solution

P ( Z < x ) = 0.17
Value of z to the cumulative probability of 0.17 from normal table is -0.954
P( x-u/s.d < 95 - Mean/9.5 ) = 0.17
That is, ( 95 - Mean/9.5 ) = -0.95
--> 95 - Mean = -0.95*9.5 => Mean = 95 - 9.025           
--> Mean = 85.975