Questions: 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 plants. He found that 39 of the 61 plants in this sample were cacti. Among the 9100 plants at that expo, 5700 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:

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 plants. He found that 39 of the 61 plants in this sample were cacti. Among the 9100 plants at that expo, 5700 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:

Transcript text: 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 plants. He found that 39 of the 61 plants in this sample were cacti. Among the 9100 plants at that expo, 5700 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) $=\square$ $\square$ $\square$ (b) Sample proportion: $\square$ $=\square$ $\square$

Solution

Solution Steps

Step 1: Calculate the Population Proportion (P)

To calculate the population proportion, we use the formula $P = \frac{X}{N}$, where $X$ is the number of individuals/items with the characteristic in the population, and $N$ is the total population size. Substituting the given values, we get $P = \frac{5700}{9100} = 0.63$.

Step 2: Calculate the Sample Proportion ($\hat{p}$)

To calculate the sample proportion, we use the formula $\hat{p} = \frac{x}{n}$, where $x$ is the number of individuals/items with the characteristic in the sample, and $n$ is the sample size. Substituting the given values, we get $\hat{p} = \frac{39}{61} = 0.64$.