Binomial Distributions

The Mean and Standard Deviation of Binomial Distributions

Learning Objectives

Calculate the mean and standard deviation of binomial distributions.

Calculating the Mean

  • We can easily calculate the mean of a binomial distribution:
  • [latex]\mu = n \times p[/latex]

Calculating the Standard Deviation

  • We can also easily calculate the standard deviation of a binomial distribution:
  • [latex]\sigma = \sqrt{n \times p \times (1-p)}[/latex]

Example 29.1

Problem Setup: Let us revisit the hotel example where we randomly sample 12 guests and the probability of any guest being from Canada is 65%. of the distribution.

Question: What are the mean and standard deviation for this problem?

Solution: Click here to download the Excel solution. Also, see the solutions below:

  • [latex]\mu = n \times p = 12 \times 0.65 = 7.8[/latex]
  • [latex]\sigma = \sqrt{n \times p \times (1-p)} = \sqrt{12 \times 0.65 \times (1-0.65)} = 1.6523[/latex]

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An Introduction to Business Statistics for Analytics (1st Edition) Copyright © 2024 by Amy Goldlist; Charles Chan; Leslie Major; Michael Johnson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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