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A certain plant runs three shifts per day. Of all the

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 22SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 22SE

A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift, 30% on the second shift, and 20% on the third shift. Of all the items produced on the first shift, 1% are defective, while 2% of the items produced on the second shift and 3% of the items produced on the third shift are defective.

a. An item is sampled at random from the day’s pro- duction, and it turns out to be defective. What is the probability that it was manufactured during the first shift?

b. An item is sampled at random from the day’s production, and it turns out not to be defective. What is the probability that it was manufactured during the third shift?

Step-by-Step Solution:

Answer:

Step 1 of 3:

                Given a certain plant runs three shifts per day.

      Let D denote the event that an item is defective.

            50% of them are produced on the first shift, let denote the event that an item is produced on the first shift.

            Therefore,  P () = 0.50.

       

          30% on the second shift.

   Let denote the event that an item is produced on the second shift.

            Therefore,  P () = 0.30.

         20% on the third shift.

 Let denote the event that an item is produced on the third shift.

            Therefore,  P () = 0.20.

 All the items produced on the first shift, 1% are the defective.

  That is, P (D/) = 0.01.

 2% of the items produced on the second shift.

  That is, P (D/) = 0.02.

3% of the items produced on the third shift.

  That is, P (D/) = 0.03.


Step 2 of 3

Chapter 2, Problem 22SE is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Since the solution to 22SE from 2 chapter was answered, more than 847 students have viewed the full step-by-step answer. The answer to “?A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift, 30% on the second shift, and 20% on the third shift. Of all the items produced on the first shift, 1% are defective, while 2% of the items produced on the second shift and 3% of the items produced on the third shift are defective.a. An item is sampled at random from the day’s pro- duction, and it turns out to be defective. What is the probability that it was manufactured during the first shift?b. An item is sampled at random from the day’s production, and it turns out not to be defective. What is the probability that it was manufactured during the third shift?” is broken down into a number of easy to follow steps, and 130 words. The full step-by-step solution to problem: 22SE from chapter: 2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: shift, produced, defective, items, day. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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