To find the standard deviation $\sigma$ for a binomial distribution, we use the formula:

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

Given:

• $n = 48$
• $p = \frac{3}{5} = 0.6$

Step-by-step calculation:

1. Compute $1 - p$: $1 - p = 1 - 0.6 = 0.4$

2. Compute $n \cdot p \cdot (1 - p)$: $n \cdot p \cdot (1 - p) = 48 \cdot 0.6 \cdot 0.4 = 48 \cdot 0.24 = 11.52$

3. Compute the square root to find $\sigma$: $\sigma = \sqrt{11.52} \approx 3.39$

Final Answer:

The correct answer is C. $\sigma = 3.39$

Would you like a detailed breakdown of other options or further clarifications? Here are some related questions you may find helpful:

1. How does the standard deviation relate to the binomial distribution?
2. What is the formula for mean in a binomial distribution?
3. How does changing $n$ affect the standard deviation in a binomial distribution?
4. How does changing $p$ affect the variance of the distribution?
5. What is the probability mass function for a binomial distribution?

Tip: Always double-check your calculations when working with square roots, as rounding can affect the