Question

xylem park hosts many expos to teach the public about plants. last years 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 organizers 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: select = (b) sample proportion: select =

Explanation:

Step1: Define population proportion formula

The population proportion $p$ is the proportion of cacti in the entire population of plants at the expo. Given that 38 out of every 61 plants were cacti. So $p=\frac{38}{61}$.

Step2: Calculate population proportion

$p=\frac{38}{61}\approx 0.62$

Step3: Define sample - proportion formula

The sample proportion $\hat{p}$ is the proportion of cacti in the sample. The sample has 91 plants and 50 of them are cacti. So $\hat{p}=\frac{50}{91}$.

Step4: Calculate sample proportion

$\hat{p}=\frac{50}{91}\approx 0.55$

Answer:

(a) Population proportion: $p = 0.62$
(b) Sample proportion: $\hat{p}=0.55$