Question

a scientist is studying tulips and daffodils. the scientist estimates that there are 150 tulips in the population of 600 tulips and daffodils. he chooses flowers from random parts of the garden to study. which best explains how he can choose a random sample of flowers to represent the population?
he can choose 50 flowers.
he can choose 25 tulips and 25 daffodils.
he can choose 15 tulips and 60 daffodils.
he can choose 10 tulips and 30 daffodils.

Explanation:

First, find the proportion of tulips in the population. There are 150 tulips out of 600 total flowers, so the proportion of tulips is $\frac{150}{600}=\frac{1}{4}$, and the proportion of daffodils is $1 - \frac{1}{4}=\frac{3}{4}$. Then check each option to see if the sample has the same proportion.
For option 1: Just choosing 50 flowers doesn't account for the proportion of each type.
For option 2: $\frac{25}{25 + 25}=\frac{1}{2}$, not the correct proportion.
For option 3: $\frac{15}{15+60}=\frac{15}{75}=\frac{1}{5}$, not correct.
For option 4: $\frac{10}{10 + 30}=\frac{10}{40}=\frac{1}{4}$ for tulips, and $\frac{30}{10+30}=\frac{3}{4}$ for daffodils, which matches the population proportion.

Answer:

He can choose 10 tulips and 30 daffodils.