https://file.aiquickdraw.com/mathbot/file/1726967054958vijrwpyc.jpg

Based on the data provided in the image, we need to solve the following problems:

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?

Here is the data table extracted from your image:

| Age Group | iPhone | Android | Other | Total |
|-----------|--------|---------|-------|-------|
| 18-34     | 180    | 214     | 134   | 528   |
| 35-54     | 190    | 189     | 77    | 456   |
| 55+       | 127    | 100     | 63    | 290   |
| **Total** | 497    | 503     | 274   | 1274  |

### Solving Part (a)
To find the proportion of cell-phone owners who have an iPhone, we divide the total number of iPhone users by the total number of cell-phone owners surveyed.

### Solving Part (b)
To calculate the distribution of ages using relative frequencies, we need to determine the proportion of each age group relative to the total number of respondents.

### Solving Part (c)
To find the percentage of cell-phone owners who are 55 or older and own an iPhone, we will focus on the intersection of these two categories.

Let's perform these calculations.Here are the results for each part of the problem:

a) The proportion of the adult cell-phone owners who have an iPhone is approximately **24.56%**.

b) The distribution of ages for adult cell-phone owners using relative frequencies is:
   - Age 18-34: **26.09%**
   - Age 35-54: **22.53%**
   - Age 55 or older: **14.33%**

c) About **6.27%** of adult cell-phone owners are 55 or older and own an iPhone.

Would you like more details on any of these calculations or have any other questions? Here are some related questions you might consider:

1. How many adult cell-phone owners do not own a smartphone from the provided categories?
2. What percentage of adult cell-phone owners use Android devices?
3. How does the distribution of smartphone types vary between the different age groups?
4. What is the ratio of iPhone to Android owners among those aged 18-34?
5. How does the popularity of "Other" phone types compare among different age groups?

**Tip:** When analyzing survey data, considering the sample size and demographic distribution can provide deeper insights into the patterns observed.

The Pew Research Center asked a random sample of 2024 adult cell-phone owners which type of cell phone they own: iPhone, Android, or other. The problem involves calculating marginal and joint relative frequencies by age groups.

Explore how to calculate marginal and joint relative frequencies based on a survey of 2024 adult cell-phone owners. This problem includes calculating the proportion of iPhone users and analyzing age group distributions using relative frequencies.

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