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A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 26 items are readied for shipment, and a sample of 5 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped. (a) What is the probability that a box containing 4 defectives will be shipped? (b) What is the probability that a box containing only 1 defective will be sent back for screening? (a) The probability that a box containing 4 defectives will be shipped is (Round to four decimal places as needed.) (b) The probability that a box containing only 1 defective will be sent back for screening is (Round to four decimal places as needed.)

A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 26 items are readied for shipment, and a sample of 5 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped. (a) What is the probability that a box containing 4 defectives will be shipped? (b) What is the probability that a box containing only 1 defective will be sent back for screening? (a) The probability that a box containing 4 defectives will be shipped is (Round to four decimal places as needed.) (b) The probability that a box containing only 1 defective will be sent back for screening is (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
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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**Acceptance Scheme for Manufacturing Quality Control** A manufacturing company employs an acceptance scheme to evaluate items from a production line before they are shipped. This scheme is a two-stage process: 1. **Preparation:** Boxes containing 26 items are prepared for shipment. 2. **Sampling:** A sample of 5 items from each box is randomly tested for defects. The conditions are as follows: - If any defective items are found in the sample, the entire box is sent back for a comprehensive 100% screening. - If no defective items are found, the box is shipped as is. The company seeks to determine the probabilities associated with two specific cases: ### Questions: **(a)** What is the probability that a box containing 4 defectives will be shipped? **(b)** What is the probability that a box containing only 1 defective will be sent back for screening? ### Solutions: **(a)** The probability that a box containing 4 defectives will be shipped is ___ (Round to four decimal places as needed). **(b)** The probability that a box containing only 1 defective will be sent back for screening is ___ (Round to four decimal places as needed). These probabilities provide insights into the efficiency of the quality control process and help in minimizing the shipment of defective products. Understanding these probabilities is crucial for improving manufacturing quality and ensuring customer satisfaction. **Note:** The specific probabilities will be calculated using the hypergeometric distribution formula, taking into account the composition of the box and the sample size. --- **Explanation of Diagrams/Graphs:** There are no diagrams or graphs provided in the text.
Transcribed Image Text:**Acceptance Scheme for Manufacturing Quality Control** A manufacturing company employs an acceptance scheme to evaluate items from a production line before they are shipped. This scheme is a two-stage process: 1. **Preparation:** Boxes containing 26 items are prepared for shipment. 2. **Sampling:** A sample of 5 items from each box is randomly tested for defects. The conditions are as follows: - If any defective items are found in the sample, the entire box is sent back for a comprehensive 100% screening. - If no defective items are found, the box is shipped as is. The company seeks to determine the probabilities associated with two specific cases: ### Questions: **(a)** What is the probability that a box containing 4 defectives will be shipped? **(b)** What is the probability that a box containing only 1 defective will be sent back for screening? ### Solutions: **(a)** The probability that a box containing 4 defectives will be shipped is ___ (Round to four decimal places as needed). **(b)** The probability that a box containing only 1 defective will be sent back for screening is ___ (Round to four decimal places as needed). These probabilities provide insights into the efficiency of the quality control process and help in minimizing the shipment of defective products. Understanding these probabilities is crucial for improving manufacturing quality and ensuring customer satisfaction. **Note:** The specific probabilities will be calculated using the hypergeometric distribution formula, taking into account the composition of the box and the sample size. --- **Explanation of Diagrams/Graphs:** There are no diagrams or graphs provided in the text.
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