To find the mean of a binomial distribution, you can use the formula:

$\mu = n \times p$

where:

• $n$ is the number of trials (in this case, the number of U.S. adults selected),
• $p$ is the probability of success on each trial (the probability that a U.S. adult thinks political correctness is a problem).

Given:

• $n = 6$
• $p = 0.78$

Now, we can calculate the mean $\mu$.The mean of the binomial distribution is $\mu = 4.68$. This means that, on average, you would expect about 4.68 out of the 6 U.S. adults to think that political correctness is a problem in America today.

Would you like more details or have any questions?

Here are some related questions you might explore:

1. What is the variance and standard deviation of this binomial distribution?
2. How does the mean change if you increase the sample size $n$ to 10 adults?
3. What is the probability that exactly 5 out of 6 adults think political correctness is a problem?
4. How would the mean change if $p$ were 0.5 instead of 0.78?
5. What is the probability that fewer than 3 adults think political correctness is a problem?

Tip: The mean of a binomial distribution gives you a measure of the central tendency, indicating the expected number of successes in a given number of trials.