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 15 tulips and 60 daffodils. he can choose 50 flowers. he can choose 25 tulips and 25 daffodils. he can choose 10 tulips and 30 daffodils.

Explanation:

Step1: Calculate the proportion of tulips in the population

The total number of flowers in the population is \(600\). The estimated number of tulips is \(150\). So the proportion of tulips is \(\frac{150}{600}=\frac{1}{4}\).

Step2: Check the proportion in each sample option

• For the option “He can choose 15 tulips and 60 daffodils”: The total number of flowers in the sample is \(15 + 60=75\). The proportion of tulips is \(\frac{15}{75}=\frac{1}{5}

eq\frac{1}{4}\).

• For the option “He can choose 50 flowers”: This option doesn't give the number of tulips and daffodils separately, so we can't calculate the proportion.
• For the option “He can choose 25 tulips and 25 daffodils”: The total number of flowers in the sample is \(25+25 = 50\). The proportion of tulips is \(\frac{25}{50}=\frac{1}{2}

eq\frac{1}{4}\).

• For the option “He can choose 10 tulips and 30 daffodils”: The total number of flowers in the sample is \(10 + 30=40\). The proportion of tulips is \(\frac{10}{40}=\frac{1}{4}\).

Answer:

He can choose 10 tulips and 30 daffodils.