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Let's work through the questions step by step based on the data in the image.

The total number of adult cell-phone owners is 2024, as shown in the table. Here's a breakdown of the values:

- **iPhone users**: 467
- **Android users**: 503
- **Other users**: 1054

### (a) What proportion of adult cell-phone owners have an iPhone?

The proportion is calculated by dividing the number of iPhone users by the total number of adult cell-phone owners:

\[
\text{Proportion of iPhone users} = \frac{467}{2024} \approx 0.2307
\]

So, approximately **23.07%** of adult cell-phone owners have an iPhone.

---

### (b) Find the distribution of ages for adult cell-phone owners using relative frequencies.

To find the relative frequency for each age group, divide the total number of adults in each age group by the overall total (2024).

1. **Ages 18–34**: 
\[
\frac{517}{2024} \approx 0.2554 \quad \text{(25.54%)}
\]
2. **Ages 35–54**: 
\[
\frac{637}{2024} \approx 0.3147 \quad \text{(31.47%)}
\]
3. **Ages 55+**: 
\[
\frac{870}{2024} \approx 0.4299 \quad \text{(42.99%)}
\]

Thus, the age distribution of cell-phone owners is:
- 18–34: 25.54%
- 35–54: 31.47%
- 55+: 42.99%

---

### (c) What percent of adult cell-phone owners are 55 or older and own an iPhone?

From the table, the number of people aged 55+ who own an iPhone is 127. To find the percentage:

\[
\frac{127}{2024} \times 100 \approx 6.27\%
\]

So, **6.27%** of adult cell-phone owners are 55 or older and own an iPhone.

---

Do you need further clarification or additional details? Here are 5 related questions to consider:

1. What is the joint relative frequency of Android users aged 18–34?
2. What percentage of cell-phone users aged 35–54 own an Android phone?
3. What is the marginal distribution of phone types (iPhone, Android, Other)?
4. What percentage of people aged 55+ use a phone that is not an iPhone or Android?
5. How would you calculate conditional relative frequencies for this dataset?

**Tip**: When calculating proportions or percentages, ensure the denominator is consistent with the population being analyzed (total, age group, etc.).

The Pew Research Center asked a random sample of 2024 adult cell-phone owners from the United States which type of cell phone they own: iPhone, Android, or other. The results were broken down by age category: (a) What proportion of the adult cell-phone owners have an iPhone? (b) Find the distribution of ages for adult cell-phone owners using relative frequencies. (c) What percent of adult cell-phone owners are 55 or older and own an iPhone?

Analyze data from the Pew Research Center on cell-phone ownership across different age groups. Learn how to calculate proportions of iPhone users, find the distribution of ages using relative frequencies, and determine the percentage of people aged 55 or older who own an iPhone.

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