In a binomail distribution, there are only two outcomes. Either a success or a failure. From the information given,
the probability of success, p = 1/3
probability of failure, q = 1 - 1/3 = 2/3
number of trials, n = 100
The formula for finding the mean of a binomial distribution is expressed as
Mean = np = 100 * 1/3
Mean = 33.33
The formula for finding the standard deviation of a binomial distribution is expressed as
[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{npq}\text{ = }\sqrt[]{100\text{ }\times\frac{1}{3}\times\frac{2}{3}} \\ \text{standard deviation = }4.71 \end{gathered}[/tex]