Question

A random sample of 20% of the teachers in a district was chosen. It was found that 40 of the teachers were female. What is the most reasonable inference about the number of teachers in the district that are female?

Answer 1

Let the population in the district = x

`\begin{gathered} Sample\text{ size}=(20)/(100)* x=0.2x \\ Female\text{ teachers }=40 \\ female\text{ proportion in sample}=female\text{ proportion in population} \\ (40)/(0.2x)=\frac{number\text{ of female}}{x} \\ Cross\text{ multiply;} \\ number\text{ of female}=(40x)/(0.2x) \\ number\text{ of female}=200 \end{gathered}`

Hence, the most reasonable inference about the number of teachers in the district that are female is about 200.