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In a survey of 1,600 adults in the Unite...

In a survey of 1,600 adults in the United States, 48% indicated that television is their primary source of news. The margin of error for the survey is `pm2.5%`. Which value is outside the interval that is likely to contains the exact percent of all adults in the United States who get the news primarily from telesion?

A

`45`

B

`47`

C

`49`

D

`50`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step-by-step, we will first determine the interval that likely contains the exact percentage of all adults in the United States who get their news primarily from television, based on the given data. ### Step 1: Identify the percentage of adults who indicated television as their primary source of news. The survey indicates that 48% of the adults surveyed indicated that television is their primary source of news. **Hint:** Look for the percentage given in the problem statement. ### Step 2: Determine the margin of error. The margin of error provided in the survey is ±2.5%. This means we will add and subtract this value from the percentage found in Step 1. **Hint:** Remember that the margin of error gives us a range around the percentage. ### Step 3: Calculate the lower limit of the interval. To find the lower limit, subtract the margin of error from the percentage: \[ \text{Lower Limit} = 48\% - 2.5\% = 45.5\% \] **Hint:** Use subtraction to find the lower boundary of the interval. ### Step 4: Calculate the upper limit of the interval. To find the upper limit, add the margin of error to the percentage: \[ \text{Upper Limit} = 48\% + 2.5\% = 50.5\% \] **Hint:** Use addition to find the upper boundary of the interval. ### Step 5: Define the interval. The interval that is likely to contain the exact percentage of all adults in the United States who get their news primarily from television is: \[ 45.5\% \text{ to } 50.5\% \] **Hint:** This interval is formed by the lower and upper limits calculated in the previous steps. ### Step 6: Identify which value is outside the interval. Now, we need to check which of the given options (45, 47, 49, or 50) falls outside the interval of 45.5% to 50.5%. - 45% is less than 45.5% (outside the interval) - 47% is within the interval - 49% is within the interval - 50% is within the interval **Hint:** Compare each option with the interval limits to see if they fall inside or outside. ### Conclusion: The value that is outside the interval is **45%**. **Final Answer:** 45

To solve the problem step-by-step, we will first determine the interval that likely contains the exact percentage of all adults in the United States who get their news primarily from television, based on the given data. ### Step 1: Identify the percentage of adults who indicated television as their primary source of news. The survey indicates that 48% of the adults surveyed indicated that television is their primary source of news. **Hint:** Look for the percentage given in the problem statement. ### Step 2: Determine the margin of error. ...
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