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TI 83 Central Limit Theorem: Overview
The Central Limit Theorem (CLT) is a way to show characteristics for the “sampling distribution of the means,” taken from a “parent population” which is created from the means of an infinite number of random population samples of size (N). It tells us that the distribution of means will be approximately normally distributed as N gets larger. In addition, the mean of the sampling distribution of the means and the standard deviation of the population means will equal the mean and standard deviation of the parent population.
The TI 83 calculator has a built in function that can help you calculate probabilities of central theorem word problems, which usually contain the phrase “assume the distribution is normal” (or a variation of that phrase).
The function, normalcdf, requires you to enter a lower bound, upper bound, mean, and standard deviation.
TI 83 Central Limit Theorem: Steps
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:If you have a question that asks for “greater than” or “less than” a certain number, enter 999999999 for the lower or upper bound. For example, if you wanted to know the probability of greater than 8 pounds you would enter:
Less than 8 pounds you would enter:
Tip: Sampling distributions require that the standard deviation of the mean is σ / √(n), so make sure you enter that as the standard deviation.
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