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, 38 out of every 61 plants were cacti. At that expo, the organizer took a sample of the plants. He found that 50 of the 91 plants in his sample 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) =
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, 38 out of every 61 plants were cacti. At that expo, the organizer took a sample of the plants. He found that 50 of the 91 plants in his sample 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) $\mathbf{\nabla}=$ $\square$
(b) Sample proportion: (Choose one) $\boldsymbol{\nabla}=$ $\square$
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 \(P = \frac{38}{61} = 0.62\).
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 \(\hat{p} = \frac{50}{91} = 0.55\).
Final Answer:
The population proportion (P) is 0.62, and the sample proportion (\(\hat{p}\)) is 0.55.