Production Quality Defective Shift Not Defective 7AM-3PM 7 113 3PM-11PM 11PM-7AM Use the given above information to fill in the next two blanks. If the two variables shift and production quality are independent, then the expected number of defectives items for the 3PM-11PM shift is (without any decimal places) 10 90 4 76 Given that this is an rxc table, what is the value for r?

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**Production Shifts and Quality Control Analysis**

A manufacturer of flash drives for data storage operates a production facility that runs on three eight-hour shifts per day.

The following contingency table shows the number of flash drives that were defective and not defective from each shift:

| Shift      | Defective | Not Defective |
|------------|-----------|---------------|
| 7AM-3PM    | 7         | 113           |
| 3PM-11PM   | 10        | 90            |
| 11PM-7AM   | 4         | 76            |

**Problem Statement:**

Using the given information, fill in the next two blanks.

If the two variables, shift and production quality, are independent, then the expected number of defective items for the 3PM-11PM shift is (without any decimal places): 
**[First Blank for Answer]**

Given that this is an r×c table, what is the value for r?
**[Second Blank for Answer]** and what is the value of c? **[Third Blank for Answer]**

**Explanation:**

To calculate the expected number of defective items for the 3PM-11PM shift, we use the formula for expected frequency in a contingency table:

Expected frequency for a cell = (Row total × Column total) / Grand total

From the table:
- Total defective items = 7 + 10 + 4 = 21
- Total items in 3PM-11PM shift = 10 + 90 = 100
- Grand total of all items = (7 + 113) + (10 + 90) + (4 + 76) = 300

For the 3PM-11PM shift's defective items:
Expected number of defective items for 3PM-11PM shift = (100 × 21) / 300 = 7

The value for r (number of rows) and c (number of columns):
- Number of rows (r) = 3 (shifts)
- Number of columns (c) = 2 (defective, not defective)
Transcribed Image Text:**Production Shifts and Quality Control Analysis** A manufacturer of flash drives for data storage operates a production facility that runs on three eight-hour shifts per day. The following contingency table shows the number of flash drives that were defective and not defective from each shift: | Shift | Defective | Not Defective | |------------|-----------|---------------| | 7AM-3PM | 7 | 113 | | 3PM-11PM | 10 | 90 | | 11PM-7AM | 4 | 76 | **Problem Statement:** Using the given information, fill in the next two blanks. If the two variables, shift and production quality, are independent, then the expected number of defective items for the 3PM-11PM shift is (without any decimal places): **[First Blank for Answer]** Given that this is an r×c table, what is the value for r? **[Second Blank for Answer]** and what is the value of c? **[Third Blank for Answer]** **Explanation:** To calculate the expected number of defective items for the 3PM-11PM shift, we use the formula for expected frequency in a contingency table: Expected frequency for a cell = (Row total × Column total) / Grand total From the table: - Total defective items = 7 + 10 + 4 = 21 - Total items in 3PM-11PM shift = 10 + 90 = 100 - Grand total of all items = (7 + 113) + (10 + 90) + (4 + 76) = 300 For the 3PM-11PM shift's defective items: Expected number of defective items for 3PM-11PM shift = (100 × 21) / 300 = 7 The value for r (number of rows) and c (number of columns): - Number of rows (r) = 3 (shifts) - Number of columns (c) = 2 (defective, not defective)
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