Mean and standard deviation
The mean of the binomial probability distribution is determined by the following formula:
μ = nπ
where π is the proportion of favorable outcomes and n is the number of events.
The standard deviation of the binomial probability distribution is determined by this formula:
What is the mean and standard deviation for a binomial probability distribution for ten coin flips of a fair coin?
Because the proportion of favorable outcomes of a fair coin falling heads (or tails) is π = 0.5, simply substitute into the formulas:
The probability distribution for the number of favorable outcomes is shown in Figure 1.
Note that this distribution appears to display symmetry. Only a binomial distribution with π = 0.5 will be truly symmetric. All other binomial distribution will be skewed.
Figure 1.The binomial probability distribution of the number of heads resulting from ten coin tosses.