Question

the distribution
median household income
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 55766 on x - axis

Estimate corresponding y - value on cumulative percent curve.

Step2: For first quartile (25th percentile)

Find x - value at y = 25 on curve.

Step3: Use z - score formula $z=\frac{x-\mu}{\sigma}$

$x = 66692$, $\mu=51742.44$, $\sigma = 8201.642$

Answer:

1. Estimated percentile from curve.
2. Estimated value from 25th percentile on curve; 25% of households have income below this.
3. $z=\frac{66692 - 51742.44}{8201.642}$; indicates how many SDs above mean.