Question

The Census Bureau gives this distribution for the number of people in American households in 2016,

Family size 1 2 3 4 5 6 7
Proportion 0.28 0.35 0.150.130.060.020.01

Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7.

Suppose you take a random sample of 1000 American households. About how many of these households will be of size 22 Sizes 3 to 7 ?
The number of households of size 2 is about _____
The number of households of size 3 to 7 is about _____

Answer 1

To estimate the number of households of a certain size in a random sample of 1000, multiply the proportion for that household size by 1000. There will be about 350 households of size 2, and about 370 households for sizes 3 to 7.

Step-by-step explanation:

The student is asking how to predict the number of households in a random sample of 1000 American households based on given proportions for different household sizes in 2016. To find the number of households of size 2, we multiply the proportion given for households of size 2 (0.35) by the total number of households in the sample (1000). Similarly, to find the number of households for sizes 3 to 7, we add the proportions for these household sizes together and then multiply by the total sample size.

For households of size 2: 0.35 × 1000 = 350 households.

For households of size 3 to 7: (0.15 + 0.13 + 0.06 + 0.02 + 0.01) × 1000 = (0.37) × 1000 = 370 households in total.

There are about 350 households of size 2 and about 370 households of sizes 3 to 7 in the sample.