Xylem Park hosts many expos to teach the public about plants. Last year's desert plant expo featured cacti. At the desert plant expo, the organizer took a sample of the  91 plants. He found that  50 of these plants were cacti. At that expo,  38 out of every 61 plants were cacti.

For the organizer's sample, find and write with proper notation the population proportion and sample proportion of plants that were cacti. Write the proportions as decimals (not percentages) rounded to two decimal places.

(a)	Population proportion:	▼(Choose one)
(b)	Sample proportion:	▼(Choose one)

To solve the problem, we need to determine both the **population proportion** and the **sample proportion** of cacti at the expo. Let's break it down:

### (a) Population Proportion:
The problem states that **38 out of every 61 plants were cacti** at the desert plant expo. So, the population proportion is the fraction of cacti among the total number of plants in the population.

\[
\text{Population proportion} = \frac{38}{61}
\]

Calculating the decimal:

\[
\frac{38}{61} \approx 0.623
\]

Rounded to two decimal places:

\[
\text{Population proportion} \approx 0.62
\]

### (b) Sample Proportion:
The organizer took a **sample of 91 plants**, and **50 of them were cacti**. The sample proportion is the fraction of cacti in this sample.

\[
\text{Sample proportion} = \frac{50}{91}
\]

Calculating the decimal:

\[
\frac{50}{91} \approx 0.549
\]

Rounded to two decimal places:

\[
\text{Sample proportion} \approx 0.55
\]

### Final Answer:
- **(a) Population proportion:** \( 0.62 \)
- **(b) Sample proportion:** \( 0.55 \)

---

Do you want further details or have any questions? 

Here are 5 questions to extend your understanding:
1. What is the difference between a population and a sample in statistics?
2. How would the proportions change if the sample size increased?
3. Why is it important to round proportions to two decimal places?
4. How would you calculate the margin of error for this sample?
5. What is the meaning of a population proportion of 0.62 in context?

**Tip:** In statistics, the **population** refers to the entire group you're studying, while the **sample** is a smaller group taken from the population to make inferences.

Xylem Park hosts many expos to teach the public about plants. Last year's desert plant expo featured cacti. At the desert plant expo, the organizer took a sample of the 91 plants. He found that 50 of these plants were cacti. At that expo, 38 out of every 61 plants were cacti. For the organizer's sample, find and write with proper notation the population proportion and sample proportion of plants that were cacti. Write the proportions as decimals (not percentages) rounded to two decimal places.

Learn how to calculate the population and sample proportions of cacti at Xylem Park's Desert Plant Expo. This example shows how to use fractions and decimals to find proportions, with 38 out of 61 plants as cacti in the population and 50 out of 91 in the sample. Suitable for students in Grades 6-8.

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