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To solve this problem, we need to use the formula for the standard deviation (\(\sigma\)) of a binomial distribution:

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

where:
- \( n \) is the number of trials (in this case, \( n = 50 \))
- \( p \) is the probability of success (in this case, \( p = 0.15 \))

Let's calculate it:

\[
\sigma = \sqrt{50 \cdot 0.15 \cdot (1 - 0.15)} = \sqrt{50 \cdot 0.15 \cdot 0.85}
\]

\[
\sigma = \sqrt{50 \cdot 0.1275} = \sqrt{6.375} \approx 2.525
\]

So, the correct answer is **B) 2.525**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the value of \( p \) affect the standard deviation of a binomial distribution?
2. What is the variance of a binomial distribution and how is it related to the standard deviation?
3. How would the standard deviation change if \( n \) was increased to 100 while keeping \( p \) the same?
4. What is the mean (\( \mu \)) of this binomial distribution, and how is it calculated?
5. What happens to the shape of a binomial distribution as \( n \) increases while \( p \) remains fixed?

**Tip:** The standard deviation of a binomial distribution increases with a larger \( n \) or when \( p \) is closer to 0.5, reflecting greater variability in outcomes.

The standard deviation of a binomial distribution for which n=50 and p=0.15 is:

Learn how to calculate the standard deviation of a binomial distribution for n=50 and p=0.15 using the formula σ = sqrt(n * p * (1 - p)). Suitable for students in Grades 9-12.

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