Exactly 1 Person Not Liking Cilantro

Oct 13, 2025 by magicalceylontours.com 142 views

The Binomial Distribution: A Statistical Approach to Understanding Cilantro Preferences

The binomial distribution is a fundamental concept in statistics that helps us understand the probability of success in a fixed number of independent trials. In this article, we will apply the binomial distribution to a real-world scenario involving cilantro preferences. We will explore how to use the binomial distribution to compute the probability of a certain number of people liking cilantro in a random sample.

A researcher takes a random sample of 15 people and surveys whether they like cilantro. We know that about 10% of people do not like the taste of cilantro. We want to use the binomial distribution to compute the probability of exactly 1, 2, 3, and 4 people not liking cilantro in the sample.

The binomial distribution formula is given by:

P(X = k) = (nCk) * (p^k) * (q^(n-k))

where:

P(X = k) is the probability of exactly k successes
n is the number of trials (in this case, 15 people)
k is the number of successes (in this case, people not liking cilantro)
p is the probability of success (in this case, 0.1 or 10%)
q is the probability of failure (in this case, 0.9 or 90%)
nCk is the number of combinations of n items taken k at a time

We will use the binomial distribution formula to compute the probabilities of exactly 1, 2, 3, and 4 people not liking cilantro in the sample.

Exactly 1 Person Not Liking Cilantro

P(X = 1) = (15C1) * (0.1^1) * (0.9^14) = 15 * 0.1 * 0.9039 = 0.1361

Exactly 2 People Not Liking Cilantro

P(X = 2) = (15C2) * (0.1^2) * (0.9^13) = 105 * 0.01 * 0.4783 = 0.0501

Exactly 3 People Not Liking Cilantro

P(X = 3) = (15C3) * (0.1^3) * (0.9^12) = 455 * 0.001 * 0.1738 = 0.0079

Exactly 4 People Not Liking Cilantro

P(X = 4) = (15C4) * (0.1^4) * (0.9^11) = 1365 * 0.0001 * 0.0662 = 0.0009

The binomial distribution provides a powerful tool for understanding the probability of success in a fixed number of independent trials. In this article, we applied the binomial distribution to a real-world scenario involving cilantro preferences. We computed the probabilities of exactly 1, 2, 3, and 4 people not liking cilantro in a random sample of 15 people.

The results show that the probability of exactly 1 person not liking cilantro is 0.1361, while the probability of exactly 4 people not liking cilantro is 0.0009. This suggests that the probability of people not liking cilantro decreases as the number of people increases.

In conclusion, the binomial distribution is a useful tool for understanding the probability of success in a fixed number of independent trials. By applying the binomial distribution to a real-world scenario involving cilantro preferences, we can gain insights into the probability of people liking or disliking cilantro. This knowledge can be useful in various fields, such as marketing, psychology, and sociology.

Johnson, N. L., & Kotz, S. (1969). Distributions in statistics: Continuous univariate distributions. Wiley.
Feller, W. (1968). An introduction to probability theory and its applications. Wiley.
Agresti, A. (2002). Categorical data analysis. Wiley.
Frequently Asked Questions: The Binomial Distribution and Cilantro Preferences

In our previous article, we explored the binomial distribution and its application to a real-world scenario involving cilantro preferences. We computed the probabilities of exactly 1, 2, 3, and 4 people not liking cilantro in a random sample of 15 people. In this article, we will address some frequently asked questions related to the binomial distribution and cilantro preferences.

Q: What is the binomial distribution?

A: The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has a constant probability of success.

Q: How is the binomial distribution used in real-world scenarios?

A: The binomial distribution is used in a wide range of real-world scenarios, including quality control, public health, marketing, and finance. In the context of cilantro preferences, the binomial distribution can be used to model the probability of people liking or disliking cilantro.

Q: What is the probability of a person liking cilantro?

A: According to our previous article, the probability of a person liking cilantro is 90% (1 - 0.1).

Q: What is the probability of a person not liking cilantro?

A: According to our previous article, the probability of a person not liking cilantro is 10% (0.1).

Q: How does the binomial distribution take into account the number of people in the sample?

A: The binomial distribution takes into account the number of people in the sample through the use of the combination formula (nCk), where n is the number of people in the sample and k is the number of people not liking cilantro.

Q: Can the binomial distribution be used to model other types of data?

A: Yes, the binomial distribution can be used to model other types of data, including binary data (e.g., 0/1, yes/no) and count data (e.g., number of successes).

Q: What are some common applications of the binomial distribution?

A: Some common applications of the binomial distribution include:

Quality control: modeling the probability of defects in a manufacturing process
Public health: modeling the probability of disease transmission
Marketing: modeling the probability of customer response to a marketing campaign
Finance: modeling the probability of stock price movements

In conclusion, the binomial distribution is a powerful tool for modeling the probability of success in a fixed number of independent trials. By understanding the binomial distribution and its applications, we can gain insights into a wide range of real-world scenarios, including cilantro preferences.

Johnson, N. L., & Kotz, S. (1969). Distributions in statistics: Continuous univariate distributions. Wiley.
Feller, W. (1968). An introduction to probability theory and its applications. Wiley.
Agresti, A. (2002). Categorical data analysis. Wiley.

For more information on the binomial distribution, see the following resources:

Wikipedia: Binomial distribution
Khan Academy: Binomial distribution
Stat Trek: Binomial distribution

For more information on cilantro preferences, see the following resources:

National Geographic: Cilantro
Science Daily: Cilantro preferences
Food Network: Cilantro recipes