A survey of 680 households asked about cable television and video streaming subscriptions.

Question

~ 540 households have a video streaming service.
~ 80% of the total households have cable television.
~ Of the households with no cable television, 7 times as many have a
streaming service as have no video streaming service.

Complete the two-way frequency table to summarize the data from the survey. (Fill in the blanks that correspond to the box number of the table.)
Video Streaming Service No Video Streaming Service Total
Cable Television left parenthesis, 1, right parenthesis(1) left parenthesis, 2, right parenthesis(2) left parenthesis, 3, right parenthesis(3)
No Cable Television left parenthesis, 4, right parenthesis(4) left parenthesis, 5, right parenthesis(5) left parenthesis, 6, right parenthesis(6)
Total 540540 left parenthesis, 7, right parenthesis(7) 680680
Answer

Answer 1

To fill in the two-way frequency table based on the information provided, let's analyze the data step by step.

1. Total number of households: 680
2. Households with video streaming: 540
3. Households with cable television: 80% of 680 = 0.80 * 680 = 544
4. Households without cable television: Total households - Households with cable television = 680 - 544 = 136

Next, we calculate the number of households that have no cable television but have a video streaming service and those that don't have a streaming service.

5. Let \( x \) be the number of households without cable television that do not have a streaming service. According to the information given, the number of households without cable television but with a streaming service is \( 7x \).

The total number of households without cable television is the sum of those with and without a streaming service: \[ x + 7x = 136 \] \[ 8x = 136 \implies x = \frac{136}{8} = 17 \] Thus, there are:

• \( x = 17 \) (no streaming service)
• \( 7x = 7 \times 17 = 119 \) (have streaming service)

Now we can fill out the table:

Table Summary:

| | Video Streaming Service | No Video Streaming Service | Total | |-----------------------------------|---------------------------|-------------------------------|------------| | Cable Television | (1) = 544 - 119 = 425 | (2) = 544 - 425 = 119 | (3) = 544 | | No Cable Television | (4) = 119 | (5) = 17 | (6) = 136 | | Total | (7) = 540 | 680 |

Now let's fill in the boxes based on our calculations:

1. (1): 425 (Cable Television + Video Streaming)
2. (2): 119 (Cable Television + No Video Streaming)
3. (3): 544 (Total Cable Television)
4. (4): 119 (No Cable Television + Video Streaming)
5. (5): 17 (No Cable Television + No Video Streaming)
6. (6): 136 (Total No Cable Television)
7. (7): 540 (Total with Video Streaming)

Putting this all together, we have:

| | Video Streaming Service | No Video Streaming Service | Total | |-----------------------------------|------------------------|----------------------------|------------| | Cable Television | 425 | 119 | 544 | | No Cable Television | 119 | 17 | 136 | | Total | 540 | 680 |

Final Values:

• (1) = 425
• (2) = 119
• (3) = 544
• (4) = 119
• (5) = 17
• (6) = 136
• (7) = 540

This completes the two-way frequency table summarizing the survey data.