To find the mean ($\mu$) of a binomial distribution, we use the following formula:

$\mu = n \cdot p$

Where:

• $n$ is the number of trials (the number of adults selected).
• $p$ is the probability of success (the probability that an adult believes that life on other planets is plausible).

Since you haven't provided the value of $p$, I'll show you the general approach. You would plug in the value of $p$ based on the percentage of adults who believe life on other planets is plausible.

For example, if 60% of adults believe life on other planets is plausible, then $p = 0.60$, and you would substitute $n = 5$ (since 5 adults were selected) into the formula.

Let's compute the mean using that example:

$\mu = 5 \cdot 0.60 = 3$

This means that, on average, 3 out of the 5 selected adults would believe that life on other planets is plausible.

If you have a different value for $p$, you can substitute that into the formula. Would you like to provide the exact percentage, or shall I continue with this example?

---

Would you like the steps for variance and standard deviation next? Here are some follow-up questions:

1. What value of $p$ (the probability) should be used for the calculation?
2. Would you like a detailed explanation of variance and standard deviation formulas?
3. Do you need help understanding how binomial distribution applies to other contexts?
4. Would you like to explore how changing $n$ affects the distribution?
5. Should we explore other methods for analyzing this type of probability problem?

Tip: The standard deviation of a binomial distribution provides a measure of how spread out the possible outcomes are, relative to the mean.