Solve the following ### Acceptance Scheme for Shipping ItemsA manufacturing company implements an acceptance scheme on items coming from a production line before they are shipped to customers. This scheme follows a two-stage inspection plan:1. **Initial Preparation:** - Boxes containing 30 items are prepared for shipment. 2. **Testing for Defectives:** - A sample of 5 items from each box is tested for defectives. - If any defective items are found within this sample, the entire box is sent back for 100% screening. - If no defectives are found in the sample, the box is shipped without further inspection.### Probability Questions(a) **What is the probability that a box containing 3 defectives will be shipped?**(b) **What is the probability that a box containing only 1 defective will be sent back for screening?**---### Calculation Expectations(a) **Probability Calculation for 3 Defectives:** - Calculate the probability that a box containing 3 defectives will be shipped without any further inspection. - Round your answer to four decimal places.(b) **Probability Calculation for 1 Defective:** - Calculate the probability that a box containing only 1 defective will be identified during the sample testing and be sent back for full screening. - Round your answer to four decimal places.

Here we will use the Hypergeometric distribution to calculate the required answer

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 30 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 box containing 3 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 3 defectives will be shipped is. (Round to four decimal places as needed.) G (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 30 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 box containing 3 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 3 defectives will be shipped is. (Round to four decimal places as needed.) G (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 First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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