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.