6.4: Binomial distribution and Normal Distribution
 Page ID
 7330
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Discrete probability distribution
Binomial Trials
1. There are a fixed number of independent trials \( n. \)
2. Each trial has only two (hence binomial) outcomes, either “success” or “failure”.
3. For the trials, the probability of a success,\( p\), is always the same, and the probability of failure, \(q=1 p\), is also always the same.
Excel Activity
Goal: Get a “feel” for binomial distributions by finding their probability distribution tables and graphing them.
Calculate the probability distribution table for X, a binomial distribution with 10 trials and probability of success p = 0.02. Use the drag feature to save yourself from a lot of typing!
X 
P(X = x) 
0 (say this is in cell A2) 
=BINOMDIST (A2, 10,0.2,False) 
1 

2 

Use Chart Wizard to plot the probabilities as a histogram (bar chart with no gaps!) You’ll need to click on the bars of the chart and Select Data to get the 0, 1, 2, … as the Xaxis labels and you’ll need to Select Format Data Series to remove gaps.
Repeat for n=10, p= 0.5 and n=10, p = 0.9. You’ll get 3 tables and 3 histograms. What are the shapes of each distribution?
Answer the following: For small n Binomial Histograms tend to be ______ skewed if p < 0.5 and ______ skewed if p > 0.5.