Download Using Minitab to Compute Binomial Probabilities

Example of How to Compute a Binomial Probability Using Minitab
Example (from Daniels, 6th ed., page 90)
Suppose that it is known that in a certain population 10% of the population is colorblind. If a random sample of
25 people is drawn from this population, compute :
1. Probability that exactly 10 people are color blind.
X (number of color blind people among the 25) has a binomial distribution with parameters n=25 and p=0.1.
Procedure to compute P[X = 10] :
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Calc > Probability Distributions > Binomial
Click on “Probability”
Number of Trials = 25
Probability of Success = 0.1
Click on “Input constant”
Write 10 in the cell to the right of “Input constant”
Click “OK”
The result should be 0.0001.
2. Probability that exactly 0, 1, 2, …, 15 people are color blind.
X (number of color blind people among the 25) has a binomial distribution with parameters n=25 and p=0.1.
Procedure to compute a set of probabilities:
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On the Worksheet, enter the numbers 0, 1, 2, …, 15 in Column C1
Calc > Probability Distributions > Binomial
Click on “Probability”
Number of Trials = 25
Probability of Success = 0.1
Click on “Input column” and enter C1
Click “OK”
The worksheet will contain the probabilities for each possible outcome.
3. Probability that five or fewer people will be color blind.
Procedure to compute P[X ≤ 5] :
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Calc > Probability Distributions > Binomial
Click on “Cumulative probability”
minitab-binprob.doc 10/16/01 9:32 AM
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Number of Trials = 25
Probability of Success = 0.1
Click on “Input constant”
Write 5 in the cell to the right of “Input constant”
Click “OK”
The result should be 0.9666.
3. Probability that between 6 and 9 inclusive will be color blind.
P[6 ≤ X ≤ 9] = P[ X ≤ 9] - P[X ≤ 5]
Procedure to compute P[X ≤ 9] :
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Calc > Probability Distributions > Binomial
Click on “Cumulative probability”
Number of Trials = 25
Probability of Success = 0.1
Click on “Input constant”
Write 9 in the cell to the right of “Input constant”
Click “OK”
The result should be 0.9999.
Therefore : P[6 ≤ X ≤ 9] = 0.9999 – 0.9666 = 0.0333.
minitab-binprob.doc 10/16/01 9:32 AM
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