Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution isQuestion 8Select one:a.1.44b.144c.12d.20

1. ### Break Down the Problem

We need to find the variance of a binomial distribution, where we know the probability of success $p = 0.4$ and the sample size $n = 50$.

2. ### Relevant Concepts

The variance $\sigma^2$ of a binomial distribution can be calculated using the formula:

$\sigma^2 = n \cdot p \cdot (1 - p)$

where:

• $n$ = number of trials (sample size)
• $p$ = probability of success
• $(1 - p)$ = probability of failure

3. ### Analysis and Detail

Let's plug the values into the formula:

$\sigma^2 = n \cdot p \cdot (1 - p) = 50 \cdot 0.4 \cdot (1 - 0.4)$

Calculating further:

1. Calculate $1 - p$: $1 - p = 1 - 0.4 = 0.6$
2. Now substitute back into the formula: $\sigma^2 = 50 \cdot 0.4 \cdot 0.6$
3. Calculate $0.4 \cdot 0.6$: $0.4 \cdot 0.6 = 0.24$
4. Finally multiply by $50$: $\sigma^2 = 50 \cdot 0.24 = 12$

4. ### Verify and Summarize

We calculated step by step and verified that the variance is $12$. Therefore, based on the options provided:

Final Answer

c. 12