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Understanding Binomial Distribution in Probability Analysis

Learn how to use binomial distribution to analyze proportions and rates in quality control scenarios. Explore the formula, assumptions, and practical examples.

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Understanding Binomial Distribution in Probability Analysis

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  1. Probability Mohamed Ubaidullah Lecturer Asia Pacific University of Technology and Innovation 22/10/15

  2. Binomial distribution It is an appropriate tool in the analysis of proportion and rates. In quality control, we assess number of defective items in a lot of goods. In this situation, binomial is to be used. You are given “n” and “p”. In this situation, binomial is to be used.

  3. P(X = r)= nCr pr (1-p) n-r r = # successes out of n trials Formula: Binomial gives number of trials which mean people or items or distinct things] and probability. n = number of trials p = probability of success Note: Binomial is discrete probability distribution because r can assume values such as 0, 1, 2, … . The each value of x has its own probability

  4. A chain of motels has adopted a policy of giving a 3% discount to customers who pay in cash rather than by credit cards. Its experience is that 30% of all customers take the discount. Let Y = number of discount takers among the next 20 customers. Do you think the binomial assumptions are reasonable in this situation? Justify your answer. Yes. we are given “n” and “p”. In this situation, binomial is to be used.

  5. At least, minimum of, no less than at least two(≥) = 1-[p(x=0)+p(x=1) At most, maximum of, no more than at most two(≤) = p(x=0)+p(x=1)+p(x=2) Is greater than, more than more than two =1-[p(x=0)+p(x=1)+p(x=2)] Is less than, smaller than, fewer than Key words in binomial distribution • less than two = p(x=0) + p(x=1)

  6. Example 1: Finding Binomial Probabilities • An Internet service provider has installed c modems to serve the needs of a population of 10 customers. It is estimated that at a given time, each customer will need a connection with probability of 0.6, independently of the others. Find the probability that • 2 customers need a connection. • More than 1customer need a connection • At least 2 customers need a connection.

  7. “More than” Probabilities: P(more than one) = 1 – P(complement of “more than one”) = 1 – P(none) – P(one)

  8. At least Probabilities: P(at least two) = 1 – P(complement of “at least two”) = 1 – P(none) – P(one)

  9. Experience has shown that 30% of the rocket launchings at a NASA base have to be delayed due to weather conditions. Determine the probability that among ten rocket launchings at that base, at most three will have to be delayed due to weather conditions Example 2: Finding Binomial Probability Solution: “At most three” means 0, 1, 2, or 3. n = 10 and p = .3 we find that p(0) + p(1) + p(2) + p(3) = .650

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