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To calculate the standard deviation for a binomial distribution, the correct formula is:

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

Where:
- \(n\) is the number of trials,
- \(p\) is the probability of success on each trial.

Looking at the options in the image:
- The correct answer is **option b**: \( \sqrt{np(1 - p)} \).

Would you like further details or have any questions about this concept?

Here are five related questions to expand your understanding:
1. What is the formula for the mean of a binomial distribution?
2. How does the probability \(p\) affect the shape of a binomial distribution?
3. What conditions allow you to approximate a binomial distribution with a normal distribution?
4. Can the standard deviation of a binomial distribution ever be larger than the number of trials \(n\)?
5. How does the variance of a binomial distribution relate to the standard deviation?

**Tip:** When approximating a binomial distribution with a normal distribution, remember to use the **continuity correction** for discrete data.

When approximating a binomial distribution, how do you calculate the standard deviation?

Learn how to calculate the standard deviation for a binomial distribution using the formula √np(1 - p). This problem involves key concepts of probability theory, including binomial distribution and the binomial theorem, suitable for students in Grades 10-12.

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