https://file.aiquickdraw.com/mathbot/file/1729710318868001pihyl.jpg

use the survey to answer questions 2 and 3

Let's go through the questions and data provided in your project:

### Question 2: Probability Calculation

From the survey, you're asked to determine the probability that someone uses ibuprofen for pain.

**Results of the survey:**
- Out of 10 people, 6 responded "Yes" to using ibuprofen.

So, the probability \( P(\text{Yes}) \) is calculated as:
\[
P(\text{Yes}) = \frac{6}{10} = 0.6 \text{ or } 60\%.
\]

This matches the 60% mentioned in the image.

### Question 3: Binomial Distribution Chart

Next, you need to use this 60% probability to draw a binomial distribution chart for a group of 15 people.

#### Parameters for the binomial distribution:
- \( n = 15 \) (the group size)
- \( p = 0.6 \) (the probability of success, where "success" means someone uses ibuprofen)
- \( q = 1 - p = 0.4 \) (the probability of failure, meaning not using ibuprofen)

The probability of \( X \) successes in \( n \) trials (where \( X \) is the number of people who use ibuprofen) in a binomial distribution is given by:
\[
P(X = k) = \binom{n}{k} p^k q^{n-k}
\]
where \( \binom{n}{k} \) is the binomial coefficient.

From the table you’ve provided:
- It shows the probabilities \( P(X) \) for different values of \( X \), where \( X \) ranges from 0 to 15.

Now, let me know if you'd like further clarification or assistance with a detailed graph or additional calculations!

---

### Further Questions for Exploration:
1. How does changing the probability \( p \) (e.g., to 70%) affect the shape of the binomial distribution?
2. What is the expected value and variance of this binomial distribution?
3. How would the distribution differ if the group size were 20 instead of 15?
4. Could you describe the shape of this binomial distribution? Is it symmetric or skewed?
5. How likely is it to get exactly 8 people who use ibuprofen in a sample of 15?

### Tip:
In binomial distributions, the expected number of successes can be easily found by multiplying the probability of success by the number of trials \( E(X) = np \).

Use the survey to answer questions 2 and 3

Solve a binomial distribution problem using a survey of 10 people on their ibuprofen usage. Learn to calculate the probability of success and use it to create a binomial distribution chart for a group of 15 people. Suitable for students in Grades 10-12.

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