Math Problem Statement
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.
Solution
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:
- : The number of trials (in this case, the number of consumers surveyed).
- : The number of successes (consumers who are comfortable with drones delivering their purchases).
- : The probability of success on a single trial (the percentage of consumers who are comfortable with drones).
- : The probability of failure on a single trial (the percentage of consumers who are not comfortable with drones).
From the problem:
- (the number of consumers randomly selected).
- (we are interested in finding the probability that exactly two consumers are comfortable).
- (since 43% of consumers are comfortable with drone deliveries).
- (since the remaining percentage, 57%, are not comfortable with drone deliveries).
Recap:
Would you like further details on how to calculate the binomial probability using these values?
Five related questions:
- How do you compute binomial probabilities?
- What are the properties of a binomial distribution?
- How do you calculate the mean and standard deviation of a binomial distribution?
- What happens if you change the value of in this problem?
- What is the difference between binomial and normal distributions?
Tip:
In a binomial distribution, as the number of trials increases, the distribution tends to look more like a normal distribution, especially when is not too close to 0 or 1.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Formulas
Binomial Probability Formula: P(X = x) = C(n, x) * p^x * q^(n - x)
C(n, x) = n! / (x! * (n - x)!)
Theorems
Binomial Theorem
Complementary Rule in Probability
Suitable Grade Level
Grades 9-12
Related Recommendation
Binomial Probability for 2 Successes in 5 Trials with Drone Delivery
Finding Probability with Binomial Distribution: Consumers Comfortable with Drone Deliveries
Calculating Binomial Probabilities for Drone Favorability Among U.S. Adults
Probability of At Most One Package Not Arriving on Time - Binomial Distribution
Probability of Exactly 3 Out of 10 Customers Buying a Magazine Using Binomial Distribution