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.