Based on a survey, assume that 29% 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 three of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
The value of n is
(Type an integer or a decimal. Do not round.)

This problem is related to the binomial distribution, where we want to find the probability of a specific number of successes (in this case, consumers comfortable with drones) in a fixed number of trials.

In the binomial distribution, the parameters are defined as follows:

- \( n \) = number of trials (number of consumers selected)
- \( x \) = number of successes (number of consumers comfortable with drones)
- \( p \) = probability of success (probability a consumer is comfortable with drones)
- \( q \) = probability of failure (probability a consumer is not comfortable with drones), where \( q = 1 - p \)

Now, we can define these values based on the problem:

- \( n \) = the number of consumers selected = 6
- \( x \) = the number of successes = 3
- \( p \) = the probability of success = 0.29 (29% of consumers are comfortable)
- \( q \) = the probability of failure = \( 1 - p = 1 - 0.29 = 0.71 \)

Thus, the value of \( n \) is **6**.

Would you like to go through the steps to find the probability next?

Here are five related questions:
1. How do we calculate the binomial probability using the values of \( n \), \( x \), \( p \), and \( q \)?
2. What is the formula for the binomial probability distribution?
3. How does increasing the number of trials \( n \) affect the probability distribution?
4. Can the value of \( p \) in binomial distribution exceed 1?
5. How does the value of \( q \) relate to \( p \) in this context?

**Tip:** The sum of the probabilities \( p \) and \( q \) in a binomial distribution always equals 1.

Based on a survey, assume that 29% 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 three of them are comfortable with delivery by drones. Identify the values of n, x, p, and q. The value of n is (Type an integer or a decimal. Do not round.)

Learn how to use the binomial distribution to find the probability that exactly three out of six consumers are comfortable with drone deliveries, given that 29% are comfortable. This page provides a step-by-step explanation of the binomial distribution formula and its parameters.

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