This is a binomial probability problem, where we are interested in the standard deviation of a binomial distribution. The binomial distribution has the following properties:

• $n$: number of trials (in this case, 12 freshmen)
• $p$: probability of success (in this case, the probability that a student believes same-sex couples should have the right to legal marital status, which is 0.716)
• $q = 1 - p$: probability of failure (i.e., the complement of the success probability, $q = 1 - 0.716 = 0.284$)

The standard deviation $\sigma$ for a binomial distribution is given by the formula:

$\sigma = \sqrt{n \cdot p \cdot q}$

Step-by-step calculation:

1. $n = 12$
2. $p = 0.716$
3. $q = 1 - 0.716 = 0.284$

Now, plug these values into the formula:

$\sigma = \sqrt{12 \cdot 0.716 \cdot 0.284}$

First, calculate the product inside the square root:

$12 \cdot 0.716 \cdot 0.284 = 2.4411$

Then, take the square root:

$\sigma = \sqrt{2.4411} = 1.5623$

Thus, the standard deviation $\sigma$ is approximately 1.5623.

Would you like any additional details or clarifications?

5 Related Questions:

1. How do you calculate the mean of a binomial distribution?
2. What is the probability that exactly 8 out of the 12 students support same-sex marriage rights?
3. How would the standard deviation change if the sample size were increased to 20 students?
4. What assumptions must hold true for a distribution to be modeled as binomial?
5. How can the normal approximation be used for a binomial distribution?

Tip:

For binomial distributions with large $n$ and probabilities close to 0.5, you can use the normal approximation for faster calculations.