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Mathematics LibreTexts

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 X-axis 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.

     

    Continuous probability distribution