Suppose that NBA players average 2241 points per game with a

Suppose that NBA players average 22.41 points per game with a standard deviation of 9.212. A random sample of 57 players is taken. There is a 91% chance that the average points per game is less than _______ points.

Solution

Normal Distribution
Mean ( u ) = 22.41
Standard Deviation ( sd )= 9.212/Sqrt(57) = 1.2202
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P ( Z < x ) = 0.91
Value of z to the cumulative probability of 0.91 from normal table is 1.341
P( x-u/s.d < x - 22.41/1.2202 ) = 0.91
That is, ( x - 22.41/1.2202 ) = 1.34
--> x = 1.34 * 1.2202 + 22.41 = 24.0463                  

There is a 91% chance that the average points per game is less than 24.0463 points.