Questions: Among teenagers, 73% prefer watching shows over the internet, rather than through cable. If you asked 29 teenagers if they preferred watching shows over the internet, rather than through cable, how many would you expect to say yes? 15 29 23 21

Among teenagers, 73% prefer watching shows over the internet, rather than through cable. If you asked 29 teenagers if they preferred watching shows over the internet, rather than through cable, how many would you expect to say yes?
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Transcript text: Question 17 2 pts (CO 3) Among teenagers, $73 \%$ prefer watching shows over the internet, rather than through cable. If you asked 29 teenagers if they preferred watching shows over the internet, rather than through cable, how many would you expect to say yes? 15 29 23 21

Solution

Solution Steps

To find the expected number of teenagers who prefer watching shows over the internet, we can use the given percentage and multiply it by the total number of teenagers surveyed.

Step 1: Convert Percentage to Decimal

Given that $73\%$ of teenagers prefer watching shows over the internet, we convert this percentage to a decimal: \[ \text{percentage\_prefer\_internet} = \frac{73}{100} = 0.73 \]

Step 2: Calculate Expected Number

We are asked to find the expected number of teenagers who prefer watching shows over the internet out of 29 surveyed. We use the formula: \[ \text{expected\_number} = \text{percentage\_prefer\_internet} \times \text{total\_teenagers\_surveyed} \] Substituting the values: \[ \text{expected\_number} = 0.73 \times 29 = 21.17 \]

Final Answer

The expected number of teenagers who prefer watching shows over the internet is approximately: \[ \boxed{21.17} \] Among the given options, the closest integer is 21. Therefore, the answer is: \[ \boxed{21} \]

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