Has been loyal I or more years, given that he or she is from the east? Has been loyal I or more years, given that he or she is from the west? Are the events "from the east" and "loyal 15 or more years" independent?

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G H and I please, Thank you

Below is the transcription of the table and questions, suitable for an educational website:

---

### Customer Loyalty Data

#### Loyalty Duration by Region (Number of Customers)

|                  | Less than 1 Year | 1-2 Years | 3-4 Years | 5-9 Years | 10-14 Years | 15 or More Years | Row Total |
|------------------|------------------|-----------|-----------|-----------|--------------|------------------|-----------|
| **East**         | 32               | 54        | 59        | 112       | 77           | 118              | 452       |
| **Midwest**      | 31               | 68        | 68        | 120       | 63           | 173              | 523       |
| **South**        | 53               | 92        | 93        | 158       | 106          | 158              | 660       |
| **West**         | 41               | 56        | 67        | 78        | 45           | 86               | 373       |
| **Column Total** | 157              | 270       | 287       | 468       | 291          | 535              | 2008      |

#### Probability Questions

1. What is the probability that a customer chosen at random:
   - (a) Has been loyal 10 to 14 years?
   - (b) Has been loyal 10 to 14 years, given that he or she is from the east?
   - (c) Has been loyal at least 10 years.
   - (d) Has been loyal at least 10 years, given that he or she is from the west?
   - (e) Is from the west, given that he or she has been loyal less than 1 year?
   - (f) Is from the south, given that he or she has been loyal less than 1 year?
   - (g) Has been loyal 1 or more years, given that he or she is from the east?
   - (h) Has been loyal 1 or more years, given that he or she is from the west?
   - (i) Are the events “from the east” and “loyal 15 or more years” independent? Explain.

---

This table provides detailed information about customer loyalty periods across different regions—East,
Transcribed Image Text:Below is the transcription of the table and questions, suitable for an educational website: --- ### Customer Loyalty Data #### Loyalty Duration by Region (Number of Customers) | | Less than 1 Year | 1-2 Years | 3-4 Years | 5-9 Years | 10-14 Years | 15 or More Years | Row Total | |------------------|------------------|-----------|-----------|-----------|--------------|------------------|-----------| | **East** | 32 | 54 | 59 | 112 | 77 | 118 | 452 | | **Midwest** | 31 | 68 | 68 | 120 | 63 | 173 | 523 | | **South** | 53 | 92 | 93 | 158 | 106 | 158 | 660 | | **West** | 41 | 56 | 67 | 78 | 45 | 86 | 373 | | **Column Total** | 157 | 270 | 287 | 468 | 291 | 535 | 2008 | #### Probability Questions 1. What is the probability that a customer chosen at random: - (a) Has been loyal 10 to 14 years? - (b) Has been loyal 10 to 14 years, given that he or she is from the east? - (c) Has been loyal at least 10 years. - (d) Has been loyal at least 10 years, given that he or she is from the west? - (e) Is from the west, given that he or she has been loyal less than 1 year? - (f) Is from the south, given that he or she has been loyal less than 1 year? - (g) Has been loyal 1 or more years, given that he or she is from the east? - (h) Has been loyal 1 or more years, given that he or she is from the west? - (i) Are the events “from the east” and “loyal 15 or more years” independent? Explain. --- This table provides detailed information about customer loyalty periods across different regions—East,
**Survey: Customer Loyalty**

Are customers more loyal in the east or in the west? The following table is based on information from Trends in the United States. The columns represent the length of customer loyalty (in years) at a primary supermarket. The rows represent regions in the United States.

*Note: The image includes textual information about a survey focused on regional customer loyalty in the U.S., but no specific table or data is visible in the text provided.*
Transcribed Image Text:**Survey: Customer Loyalty** Are customers more loyal in the east or in the west? The following table is based on information from Trends in the United States. The columns represent the length of customer loyalty (in years) at a primary supermarket. The rows represent regions in the United States. *Note: The image includes textual information about a survey focused on regional customer loyalty in the U.S., but no specific table or data is visible in the text provided.*
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