Question

randy is starting a beehive so that he can have fresh honey. he decides to check the current population of bees in the hive by marking 150 bees. later, randy collects 240 bees and observes that 30 of them are marked. what is the best estimate for the bee population?

Explanation:

Step1: Set up the proportion

Let \( N \) be the total bee population. The proportion is \(\frac{\text{marked in first sample}}{\text{total in first sample}}=\frac{\text{marked in second sample}}{\text{total in second sample}}\). Here, first sample: marked \( m_1 = 150\), total \( n_1=N\); second sample: marked \( m_2 = 30\), total \( n_2 = 240\). So \(\frac{150}{N}=\frac{30}{240}\).

Step2: Solve the proportion for \( N \)

Cross - multiply: \(30N=150\times240\). Then \(N=\frac{150\times240}{30}\). Calculate \(150\times240 = 36000\), and \(\frac{36000}{30}=1200\).

Answer:

A. 1,200