Question

The cumulative relative frequency graph describes the distribution of median household incomes in the 50 states in a recent year. Given are summary statistics for the state median household incomes. North Carolina had a median household income of $41,553.

Find and interpret the -score for North Carolina

Answer 1

The z-score for North Carolina's median household income is -8.447, indicating that it is below the mean of the distribution.

Step-by-step explanation:

To find this, we need to first list the incomes in ascending order and then divide the group into quintiles (groups of two in this case, since 10 divided by 5 quintiles = 2 persons per quintile). The total income needs to be calculated by adding all individual incomes together. Afterward, the income for each quintile can be added and divided by the total income to find the share of total income that each quintile receives.

To find the z-score for North Carolina's median household income, we need to compare it to the mean and standard deviation of the distribution of median household incomes.

Let's say the mean of the distribution is $50,000 and the standard deviation is $10,000. To find the z-score, we use the formula: z = (x - μ) / σ.

Substituting the values: z = (41553 - 50000) / 10000 = -8.447. The z-score for North Carolina is approximately -8.447.

The negative sign indicates that North Carolina's median household income is below the mean of the distribution.