**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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3. If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A N B) = %3D .30 .15 .20
Q. 4 Let A, B, and C, be independent events with probabilities Par Pp, Pc of occurring, respectively. (i) What is the probability all 3 events occurring? (ii) What is the probability of none of them occurring? (iii) What is the probability that exactly 1 occurs?
Suppose A and B are two events with probabilities: P(A°) = .25, P(B) = .35, P(AN B) = .30. a) What is (A|B) ? b) What is (B|A) ?
1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier? 2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins ifa. A answers the first question, b. B answers the first question. 3. Patients are recruited onto the two arms (0 - Control,1-Treatment) of a clinical trial. The probability that an adverse outcome occurs on the…
Q.No.3. (a) A bag contains 12 balls, 4 of which are red, 3 black and 5 green. Three balls are drawn from the bag. Find the probability that (i) all three are green (ii) The first is red, second is green and third is black. (b) A sale person has a 40% chance of making a sale to any customer who is called upon. If 18 calls are made, what is the probability that (i) at most 3 sales are made (ii) at least 17 sales are made.
Suppose that E and F are two events and that P(E and F) = 0.5 and P(E)=0.8. What is P(FIE)? P(FE) = (Type an integer or a decimal.)
20. A shipment of 100 tires from the Apex Tire Corporation is known to contain 20 defective tires. Five tires are selected at random and each tire is replaced before the next tire is selected. What is the probability of getting 2 defective tires? [Do not solve] Treating this as a binomial distribution, in this problem what is the value of q n X р
Suppose a dresser drawer has blue shirts, yellow shirts, red shirts, and green shirts so that if a shirt is pulled from the drawer at random, each color has an equal chance of being drawn. P(Green) = P(Blue) = P(Red) = P(Yellow) = ¼. Complete parts (a) – (d) to create a probability distribution for the number of yellow shirts if two shirts are pulled from the drawer at random (replacing the shirt after each draw). a. List each possible outcome for the colors of the shirts if two shirts are drawn randomly from the drawer. The teacher said there should be total of 16 outcomes, not 9 or 10. In my original answer, I have 10 outcomes when there should be 16. c.Find the probability of each event (not the probability from each outcome) from part (b). For my first answer, I had the probability of each outcome, and I should have the probability of each event.
If ? and ? are two mutually exclusive events with ?(?)=0.2 and ?(?)=0.7, find the following probabilities: by the way, what's the c and d mean like Both A and B have A horizontal line over their heads
19
A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect. The process improvement team agrees that the sample contains 27 bad items and 153 good items. The team gives the items to a “certified” operator for inspection. The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly. What is the probability that the inspector will reject an item? P(inspector will reject an item) = ________%. Enter value using one decimal place.

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