Question

application 1.9 which states are rich? the cumulative relative frequency graph and the numerical summaries below describe the distribution of household incomes in the 50 states in a recent year. use the information provided to help you answer the following questions. 1. at what percentile is north dakota, with a household income of $55,766? 2. estimate and interpret the first quartile q1 of the distribution. 3. find and interpret the standardized score (z - score) for new jersey, with a household income of $66,692.

Explanation:

Step1: Locate value on graph

Find 55766 on x - axis of cumulative relative - frequency graph to estimate percentile.

Step2: Estimate Q1

Q1 is 25th percentile. Estimate from graph where cumulative relative frequency is 25%.

Step3: Calculate z - score

Use formula $z=\frac{x - \mu}{\sigma}$, where $x = 66692$, $\mu=51742.44$, $\sigma = 8210.642$.

Answer:

1. Estimated percentile from graph.
2. Estimated value from graph and interpretation as 25th percentile.
3. $z=\frac{66692 - 51742.44}{8210.642}\approx1.82$; interpretation: New Jersey's income is about 1.82 standard deviations above the mean.