Find the standard deviation of the binomial distribution.

The standard deviation of a binomial distribution can be found using the formula:

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

where:

- \(n\) is the number of trials,
- \(p\) is the probability of success on a single trial,
- \((1 - p)\) is the probability of failure.

### Steps to find the standard deviation:
1. Identify the number of trials \(n\).
2. Determine the probability of success \(p\).
3. Substitute these values into the formula.
4. Calculate the square root of the product \(n \cdot p \cdot (1 - p)\).

Would you like an example or further explanation?

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Here are 5 related questions to explore further:

1. How is the mean of a binomial distribution calculated?
2. What is the variance of a binomial distribution, and how is it related to the standard deviation?
3. Can you explain the conditions under which a binomial distribution approximates a normal distribution?
4. What happens to the standard deviation if the probability \(p\) increases?
5. How does increasing the number of trials \(n\) affect the shape of the binomial distribution?

**Tip**: The larger the number of trials \(n\), the closer the binomial distribution can resemble a normal distribution if the success probability is not too extreme.

Learn how to find the standard deviation of a binomial distribution using the formula σ = √(n * p * (1 - p)). This explanation covers key concepts such as probability, binomial distribution, and step-by-step instructions on calculating the standard deviation. Suitable for Grades 10-12.

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