**Problem 5: Probability Analysis Using Binomial and Poisson Distributions***Scenario:*Assume 100 steel rods are selected randomly from a large box containing more than 10,000 steel rods. It is estimated that 5% of these rods are defective. The probabilities for various events are calculated using the binomial distribution.*Probabilities:*- **P(A):** Probability that none of the 100 rods is defective = 0.0059- **P(B):** Probability that exactly 1 rod is defective = 0.0371- **P(C):** Probability that no more than 2 rods are defective = 0.1183- **P(D):** Probability that exactly 5 rods are defective = 0.1800- **P(E):** Probability that more than 5 rods are defective < 2.1 * 10⁻⁸*Task:*Use the Poisson distribution to compute approximations for the same probabilities. Here, use a lambda value (λ) of 5, calculated as 5% of 100 (0.05 * 100). e. P(E: more than 5 are defective)

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Answered: 5. Suppose 100 steel rods are chosen at…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In 1996, McDonald's estimated that 10% of all American workers had worked at McDonald's at one point in their career (www.businessinsider.co m). Assume that 6 American workers are randomly selected, and that this can be modeled as a binomial distribution. What is the probability that exactly 2 of the 6 workers has worked at McDonald's? T T T Arial v 3 (12pt) v T- = - E -
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11. Customers are charged incorrectly for 1 out of every 30 items, on average. Suppose a customer purchases 15 items. Find the following binomial probabilities: a. A customer is charged incorrectly on 3 items b. A customer is not charged incorrectly for any items C A customer is charged incorrectly for at least one item.
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Jaylen surveys 85 students at random to determine the proportion of students who have attended Mt. San Jacinto College for more than two years. Suppose that, in reality, 32% of students have attended for more than two years. How are the collection of all sample proportions of samples of size 85 distributed? N(__,__) 2. What is the probability that fewer than 21% of students in Jaylen's sample have been enrolled for more than two years? List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. There is a ___ chance that fewer than 21% of students in Jaylen's sample have been enrolled for more than two years. What is the probability that more than 41% of students in Jaylen's sample have been enrolled for more than two years? List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. There is a ___ chance that more than 41% of students…
An adult citizen in the Springfield region has about 0.3 chance of being selected for jury duty. If jury members are selected randomly and the Samuelson Company in Springfield has seven workers, what is the probability of the scenarios below? (Hint: You may use the binomial individual and cumulative tables attached.) Please include only a numerical response. Each response must have five numbers (a decimal to the ten-thousandths place). 1. None of the workers will be selected. 2. Exactly one of the Samuelson Company workers will be selected. 3. Fewer than four workers will be selected. 4. Between four and seven workers will be selected.
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