small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data is attached as a picture. Answer the following: 1. What is the probability that an employee chose online training? 2. What is the probability that an employee is in the quality division and chose online training? 3. What is the probability that an employee chose online training given that he/she is in the sales division? 4. Does it appear that choice of instructional method (traditional or online) and division (sales, quality and operations) are independent? a) No, they are no independent. b) Yes, they are independent.

small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data is attached as a picture. Answer the following: 1. What is the probability that an employee chose online training? 2. What is the probability that an employee is in the quality division and chose online training? 3. What is the probability that an employee chose online training given that he/she is in the sales division? 4. Does it appear that choice of instructional method (traditional or online) and division (sales, quality and operations) are independent? a) No, they are no independent. b) Yes, they are independent.

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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Question

A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data is attached as a picture.

Answer the following:

1. What is the probability that an employee chose online training?

2. What is the probability that an employee is in the quality division and chose online training?

3. What is the probability that an employee chose online training given that he/she is in the sales division?

4. Does it appear that choice of instructional method (traditional or online) and division (sales, quality and operations) are independent?

a) No, they are no independent.

b) Yes, they are independent.

The table provides a comparison of different sectors for Traditional and Online categories across Sales, Quality, and Operations, along with their respective totals.

| | Sales | Quality | Operations | Total |
|-------------------------|-------|---------|------------|-------|
| **Traditional** | 16 | 10 | 8 | 34 |
| **Online** | 35 | 23 | 44 | 102 |
| **Total** | 51 | 33 | 52 | 136 |

Explanation:
- **Sales**: Traditional (16), Online (35), Total (51)
- **Quality**: Traditional (10), Online (23), Total (33)
- **Operations**: Traditional (8), Online (44), Total (52)
- **Overall Totals**: Traditional (34), Online (102), Combined (136)

This table illustrates the distribution of efforts or results in each sector, indicating a higher overall performance in the Online category compared to the Traditional one.

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