The binomial distribution with p = 1/4 has a standard deviation of 3.For this distribution,there are n = 36 scores in the sample.

Question

The binomial distribution with p = 1/4 has a standard deviation of 3.For this distribution,there are n = 36 scores in the sample.​

Quizplus · Accepted Answer

The standard deviation ($\sigma$) of a binomial distribution is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1 - p)}$, where $n$ is the number of trials and $p$ is the probability of success on each trial. For $n = 36$ and $p = 1/4$, the standard deviation is $\sigma = \sqrt{36 \cdot \frac{1}{4} \cdot \left(1 - \frac{1}{4}\right)} = \sqrt{36 \cdot \frac{1}{4} \cdot \frac{3}{4}} = \sqrt{27} = 3\sqrt{3}$, which is not equal to 3.

The Binomial Distribution with P = 1/4 Has a Standard