78% ​ of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. 

find the mean of the binomial distribution

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.

Understand how to calculate the mean of a binomial distribution using the example of U.S. adults' opinions on political correctness. Given a sample size of 6 adults and a probability of 0.78, learn how to apply the binomial distribution mean formula step-by-step. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation