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. New Jersey had a standardized score of
1.82.
Find New Jersey's median household income for that
year.
$51,742.44
$36,799.08
$64,952.36
$66,685.80
O $51,740.62
80
60
-
Cumulative relative frequency (%)
40
20
0
35 40 45 50 55 60 65 70 75
Median household income ($1000s)
11
Mean SD Min
Med Q3 Max
50 51,742.44 8210.64 36,641 46,071 50,009 57,020 71,836

Answer 1

Using z-scores, it is found that the New Jersey's median household income for that  year was of $66,685.80 .

--------------------------------

The z-score for a measure X in a data-set with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

In this problem:

• The mean is of $51,742.44, thus $\mu = 51742.44$.
• The standard deviation is of $8,210.64, thus $\sigma = 8210.64$.
• The standardized score for the median New Jersey household income is $Z = 1.82$, thus, this measure is of X.

$Z = \frac{X - \mu}{\sigma}$

$1.82 = \frac{X - 51742.44}{8210.64}$

$X - 51742.44 = 1.82(8210.64)$

$X = 66685.60$

Then, the New Jersey's median household income for that  year was of $66,685.80 .

A similar problem is given at https://brainly.com/question/16645591