The Mean and Standard Deviation of Binomial Distributions

Calculating the Mean

• We can easily calculate the mean of a binomial distribution:
• $\mu = n \times p$

Calculating the Standard Deviation

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

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:

• $\mu = n \times p = 12 \times 0.65 = 7.8$
• $\sigma = \sqrt{n \times p \times (1-p)} = \sqrt{12 \times 0.65 \times (1-0.65)} = 1.6523$