To find the variance of a binomial distribution, we need to know the following parameters:

1. $n$: The number of trials (in this case, the number of adults selected).
2. $p$: The probability of success (in this context, the probability that an adult believes that life on other planets is plausible).

The formula for the variance of a binomial distribution is:

$\text{Variance} = \sigma^2 = n \cdot p \cdot (1 - p)$

Step-by-Step Solution

1. Given Information:

   • Number of trials, $n = 5$ (since you are selecting 5 adults).
   • Probability of success, $p$ (probability that an adult believes in life on other planets).

2. Variance Calculation:

   • The variance is calculated as:

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

To calculate the variance, you need the value of $p$, the probability of success. If you provide the probability $p$, I can compute the exact variance.

If $p$ is given, for example:

• If $p = 0.6$, then:

$\sigma^2 = 5 \cdot 0.6 \cdot (1 - 0.6) = 5 \cdot 0.6 \cdot 0.4 = 1.2$

Please provide the value of $p$ to calculate the variance accurately.

Would you like me to proceed with an example, or do you have the specific probability value?