Question

10. It is claimed that 1/3 of all soda cans leak. A sample of 100 soda cans is selected. Calculatethe mean and standard deviation of the resulting binomial distribution

Answer 1

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

`\begin{gathered} \text{standard deviation = }\sqrt[]{npq}\text{ = }\sqrt[]{100\text{ }*(1)/(3)*(2)/(3)} \\ \text{standard deviation = }4.71 \end{gathered}`