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: $0.55$

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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.