Based on a​ survey, assume that

4343​%

of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when

sixsix

consumers are randomly​ selected, exactly

twotwo

of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

In this problem, you're working with a binomial probability distribution, which is used to model the number of successes in a fixed number of independent trials when each trial has the same probability of success.

The key values you need to identify are:

- \( n \): The number of trials (in this case, the number of consumers surveyed).
- \( x \): The number of successes (consumers who are comfortable with drones delivering their purchases).
- \( p \): The probability of success on a single trial (the percentage of consumers who are comfortable with drones).
- \( q \): The probability of failure on a single trial (the percentage of consumers who are **not** comfortable with drones).

From the problem:

1. \( n = 6 \) (the number of consumers randomly selected).
2. \( x = 2 \) (we are interested in finding the probability that exactly two consumers are comfortable).
3. \( p = \frac{43}{100} = 0.43 \) (since 43% of consumers are comfortable with drone deliveries).
4. \( q = 1 - p = 1 - 0.43 = 0.57 \) (since the remaining percentage, 57%, are **not** comfortable with drone deliveries).

### Recap:
- \( n = 6 \)
- \( x = 2 \)
- \( p = 0.43 \)
- \( q = 0.57 \)

Would you like further details on how to calculate the binomial probability using these values?

### Five related questions:
1. How do you compute binomial probabilities?
2. What are the properties of a binomial distribution?
3. How do you calculate the mean and standard deviation of a binomial distribution?
4. What happens if you change the value of \( x \) in this problem?
5. What is the difference between binomial and normal distributions?

### Tip:
In a binomial distribution, as the number of trials \( n \) increases, the distribution tends to look more like a normal distribution, especially when \( p \) is not too close to 0 or 1.

Based on a survey, assume that 43% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when six consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.

Explore how to calculate the probability that exactly 2 out of 6 randomly selected consumers are comfortable with drone deliveries, given that 43% of people prefer this option. Learn how to use the binomial probability formula and the binomial theorem to solve this real-world problem. Ideal for students in Grades 9-12.

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