The TI 83 calculator has a built in function that can help you calculate probabilities of central theorem word problems. The function, normalcdf, requires you to enter a lower bound, upper bound, mean, and standard deviation.
Sample problem: A fertilizer company manufactures organic fertilizer in 10 pound bags with a standard deviation of 1.25 pounds per bag. What is the probability that a random sample of 15 bags will have a mean between 9 and 9.5 pounds?
Step 1: 2nd VARS, 2.
Step 2: Enter your variables (lower bound, upper bound, mean, and standard deviation): 9 , 9 . 5 , 1 0 , ( 1 . 2 5 / 2nd x2 1 5 ) ).
Step 3: Press ENTER. This returns the probability of .05969, or .05969%.
Tip: Sampling distributions require that the standard deviation of the mean is σ / √(n), so make sure you enter that as the standard deviation.