Download THE CENTRAL LIMIT THEOREM

THE CENTRAL LIMIT THEOREM.
To demonstrate the Central Limit Theorem, let´s take 300 samples of size 100 (that is, n=100) from a
Binomial Distribution with p = 0.20, calculate the mean of each of these 300 samples, and draw the
histogram of these 300 means. That histogram should approximate the sampling distribution of X .
Solution.
GENERATING SAMPLES.
Step 1. Press the key that reads MATH.
Step 2. Now, go to PRB
Step 3. Go to 7: randBin( and press ENTER.
Step 4. Type 100, 0.2,300)
Step 5. Press the key that reads STO> , then press 2ND and 1
Step 6. Press ENTER and wait 8 minutes...
FINDING AVERAGES.
Step 1. Press 2ND and 1
Step 2. Divide L1 by 100, then press STO> and 2ND followed by 2.
Step 3. Finally, press ENTER.
MAKING HISTOGRAM.
Step 1. Press 2ND and Y=
Step 2. Press ENTER.
Step 3. Highlight the icon corresponding to histogram and replace L1 by L2 (just highlight L1, then press
2ND and 2).
Step 4. Press ZOOM and then 9.
FINDING MEAN AND STANDARD DEVIATION.
Let us find the mean and standard deviation for our 300 sample means.
Step 1. Press STAT.
Step 2. Go to CALC
Step 3. Highlight 1: 1-Var Stats and press ENTER.
Step 4. Press 2ND and 2, then press ENTER.