Question

children in 50 households
number of children number of households
0 5
1 11
2 13
3 10
4 9
5 2
using a proportion, what can you infer about the number of households in her town that have more than three children?
about 242 households have more than three children.
about 269 households have more than three children.
about 296 households have more than three children.
about 565 households have more than three children.

Explanation:

Step1: Calculate number of households with more than 3 children in sample

In the sample of 50 households, the number of households with 4 children is 9 and with 5 children is 2. So the number of households with more than 3 children in the sample is $9 + 2=11$.

Step2: Set up the proportion

Let the total number of households in the town be assumed as 1315 (a common - sense assumption when no other information about town size is given, as we need a value to work with for proportion. If this was part of a larger problem, this value should be given explicitly). Let $x$ be the number of households in the town with more than 3 children. The proportion is $\frac{11}{50}=\frac{x}{1315}$.

Step3: Solve the proportion for $x$

Cross - multiply: $50x=11\times1315$. Then $x=\frac{11\times1315}{50}=\frac{14465}{50}=289.3\approx296$ (rounding to the nearest whole number).

Answer:

About 296 households have more than three children.