Week 4 Binomial Distribution Illustrated By Bethany Mueller

Week 4 Binomial Distribution Illustrated By Bethany Muellerhtmlweek 5

Extracted from the provided content, the core assignment involves explaining the application of the binomial distribution, particularly how to compute probabilities in Excel using the BINOM.DIST (or binomdist) function. The instructions specify performing calculations for different scenarios such as exact probability, less than, greater than, and cumulative probabilities, with concrete examples involving survey data and Excel formulas.

Paper For Above instruction

The binomial distribution is a fundamental statistical tool used to model the probability of a specific number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. This distribution is particularly useful in situations where outcomes are binary—success or failure—and the number of trials is known in advance. Its application spans various fields, including business, medicine, psychology, and social sciences, providing insightful predictions that inform decision-making processes.

A typical real-world example is assessing the likelihood of a certain number of successes in a set of experiments or surveys. In the context of the example provided, a survey indicated that 17% of adults dislike Marshmallow Fluff. If a researcher randomly selects four adults and asks whether they dislike the product, the binomial distribution can be used to answer several probability questions about their responses.

To compute these probabilities, Excel’s BINOM.DIST function (or older versions’ binomdist command) offers an efficient way to perform calculations. The syntax for the function is BINOM.DIST(number_s, trials, probability_s, cumulative), where:

  • number_s: the number of successes
  • trials: total number of trials
  • probability_s: probability of success on each trial
  • cumulative: a logical value that determines the form of the function's output. If TRUE, BINOM.DIST returns the cumulative probability P(X ≤ x). If FALSE, it returns the probability mass function P(X = x).

Applying this to the example, if we denote "disliking Marshmallow Fluff" as success, then:

  • n = 4 (number of adults selected)
  • P = 0.17 (probability an adult dislikes Fluff)
  • X varies depending on the scenario

Example calculations in Excel include:

  1. Probability that exactly two of them dislike Fluff: Use =BINOM.DIST(2, 4, 0.17, FALSE). This computes P(X=2), the probability that exactly two adults dislike Fluff.
  2. Probability that fewer than two dislike Fluff: Use =BINOM.DIST(1, 4, 0.17, TRUE). This sums probabilities for 0 and 1 dislikes, giving P(X
  3. Probability that at least two dislike Fluff: Use =1 - BINOM.DIST(1, 4, 0.17, TRUE). Here, 1 represents the highest number less than 2; subtracting from 1 yields P(X≥2).
  4. Probability that two or fewer dislike Fluff: Use =BINOM.DIST(2, 4, 0.17, TRUE), which sums probabilities for 0, 1, and 2 dislikes.

Similarly, a separate example demonstrates calculating binomial probabilities for n=10 trials with P=0.6 using Excel formulas such as:

  • =BINOM.DIST(4,10,0.6,FALSE) for exactly 4 successes
  • =BINOM.DIST(4,10,0.6,TRUE) for the probability of 4 or fewer successes
  • =BINOM.DIST(3,10,0.6,TRUE) for fewer than 4 successes
  • =1 - BINOM.DIST(3,10,0.6,TRUE) for at least 4 successes

This practical use of binomial distribution allows researchers and data analysts to interpret the likelihood of various outcomes in binary experiment contexts. Proper understanding and application of Excel functions streamline the process, making it accessible and efficient for both educational and professional purposes. Mastery of these formulas aids in making informed predictions, testing hypotheses, and conducting risk assessments across numerous disciplines.

References

  • Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.). Wiley.
  • Mooney, C. Z., & Duval, R. D. (1993). Bootstrapping: A Nonparametric Approach to Statistical Inference. Sage Publications.
  • Weiss, N. A. (2012). Introductory Statistics (9th ed.). Pearson.
  • Naresh, M. R. (2008). Applied Statistics and Probability for Engineers (6th ed.). Pearson.
  • Excel Help Documentation. (2023). Microsoft Support. https://support.microsoft.com/en-us/excel
  • Agresti, A. (2018). Statistical Methods for the Social Sciences. Pearson.
  • McClave, J. T., & Sincich, T. (2017). A First Course in Statistics (13th ed.). Pearson.
  • Ross, S. M. (2014). Introduction to Probability Models. Academic Press.
  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
  • Kirk, R. E. (2013). Experimental Design: Procedures for the Behavioral Sciences. Sage Publications.

Related Assignments