Question

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

Family size 1 2 3 4 5 6 7
Proportion 0.28 0.35 0.15 0.13 0.06 0.02 0.01

Suppose you take a random sample of 2000 American bouseholds. About how many of these households will be of Size 27?

Answer 1

In a random sample of 2000 American households, about 20 households will be of size 7, as calculated by multiplying the sample size by the proportion of households of that size (2000 × 0.01).

Step-by-step explanation:

The question asks us to estimate the number of households in a sample that would be of size 7 given a distribution of household sizes in American households. To calculate this, we will multiply the proportion for households of size 7 by the total number of households in the sample.

The proportion for household size 7 is 0.01. We have a sample size of 2000 households. The calculation would be:

• Number of households of size 7 = Sample size × Proportion for size 7
• Number of households of size 7 = 2000 × 0.01
• Number of households of size 7 = 20

To find the approximate number of households of size 27 in a random sample of 2000 American households, we can use the given distribution. The proportion of households of size 7 or greater is 0.01. So, we can assume that approximately 0.01 or 1% of the households in the sample will be of size 7 or greater.

Therefore, out of 2000 households, about 1% of them or 20 households will be of size 7 or greater. Since we are assuming that 7 represents households of size exactly 7, we can conclude that approximately 20 households in the sample will be of size 27.

Thus, in a random sample of 2000 American households, we would expect about 20 households to be of size 7.