A streaming service randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week.  Of those surveyed, 45 watch more than 10 hours per week.  Based on the data, if the company has 2,500 subscribers, then how many watch more than 10 hours per week?

To solve this problem, we need to use the information given from the sample to estimate the total number of subscribers who watch more than 10 hours per week.

### Step-by-Step Solution:

1. **Find the proportion of subscribers in the sample who watch more than 10 hours per week:**

   The proportion can be calculated by dividing the number of subscribers who watch more than 10 hours by the total number of subscribers surveyed.

   \[
   \text{Proportion} = \frac{\text{Number of subscribers watching more than 10 hours}}{\text{Total number of subscribers surveyed}}
   \]

   Substituting the given values:

   \[
   \text{Proportion} = \frac{45}{100} = 0.45
   \]

   This means that 45% of the subscribers surveyed watch more than 10 hours per week.

2. **Use the proportion to estimate the number of all subscribers who watch more than 10 hours per week:**

   To estimate this number for the entire subscriber base of 2,500, multiply the proportion by the total number of subscribers:

   \[
   \text{Estimated number} = \text{Proportion} \times \text{Total number of subscribers}
   \]

   Substituting the values:

   \[
   \text{Estimated number} = 0.45 \times 2500 = 1125
   \]

### Conclusion:

Based on the sample data, it is estimated that **1,125 subscribers** watch more than 10 hours of shows per week.

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Here are 5 related questions to expand on this concept:

1. How would the estimate change if 60 out of 100 surveyed watched more than 10 hours per week?
2. What is the margin of error in this estimate if it were a confidence interval?
3. If the total number of subscribers increased to 5,000, how many would you estimate watch more than 10 hours per week?
4. What statistical assumptions are made when using a sample to estimate a population proportion?
5. How would you compute the proportion if the number of hours were categorized differently (e.g., 5-10 hours, 10-15 hours, etc.)?

**Tip:** When estimating a population parameter from a sample, remember that larger sample sizes generally lead to more accurate estimates!

A streaming service randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed, 45 watch more than 10 hours per week. Based on the data, if the company has 2,500 subscribers, then how many watch more than 10 hours per week?

Estimate how many subscribers watch more than 10 hours per week using data from a sample of 100 subscribers, with 45 reporting over 10 hours of viewing. This example covers proportion, estimation, and sampling concepts, and applies to a total subscriber base of 2,500. Suitable for students in Grades 7-9.

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