**Probability and Statistics: Binomial Distribution**_Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the standard deviation?_To find the standard deviation of a binomial distribution, we can use the formula:\[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \]where:- $ n $ is the number of trials.- $ p $ is the probability of success in a single trial.Given that:\[ n = 100 \]\[ p = \frac{1}{2} \]We substitute the values into the formula:\[ \sigma = \sqrt{100 \cdot \frac{1}{2} \cdot \left(1 - \frac{1}{2}\right)} \]\[ \sigma = \sqrt{100 \cdot \frac{1}{2} \cdot \frac{1}{2}} \]\[ \sigma = \sqrt{100 \cdot \frac{1}{4}} \]\[ \sigma = \sqrt{25} \]\[ \sigma = 5 \]Therefore, the standard deviation of the binomial distribution under the given conditions is 5.There are no graphs or diagrams in this image.

Given that, n=100 p=1/2 =0.5 Standard deviation=?

Answered: Assume you have a binomial…

Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the standard deviation?

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Estimation

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Question

**Probability and Statistics: Binomial Distribution**

_Assume you have a binomial distribution. In an experiment with 100 trials and a probability of a success equal to one half, what is the standard deviation?_

To find the standard deviation of a binomial distribution, we can use the formula:

\[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \]

where:
- $ n $ is the number of trials.
- $ p $ is the probability of success in a single trial.

Given that:
\[ n = 100 \]
\[ p = \frac{1}{2} \]

We substitute the values into the formula:

\[ \sigma = \sqrt{100 \cdot \frac{1}{2} \cdot \left(1 - \frac{1}{2}\right)} \]
\[ \sigma = \sqrt{100 \cdot \frac{1}{2} \cdot \frac{1}{2}} \]
\[ \sigma = \sqrt{100 \cdot \frac{1}{4}} \]
\[ \sigma = \sqrt{25} \]
\[ \sigma = 5 \]

Therefore, the standard deviation of the binomial distribution under the given conditions is 5.

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