91Ó°ÊÓ

The table is

Value, $x=41,553$

Mean, $\overline{x}=51,742.44$

Standard deviation, $SD=8210.64$

The formula used:$z=\frac{(value-mean)}{(s\tan darddeviation)}$

The $z-$score is the number of standard deviations a value deviates from the mean.

The value above the mean is indicated by a positive $z-$score.

Whereas,

The value below the mean is indicated by a negative $z-$score.

Calculate the $z-$ score:

$z=\frac{x−x}{SD}=\frac{41,553−51,742.44}{8210.64}=\frac{−10,189.44}{8210.64}≈−1.24$

Therefore,

North California's median household income is $1.24$ standard deviations lower than the mean of all $50$ states' median household incomes.

The $z-$score is the number of standard deviations a value deviates from the mean.

The value above the mean is indicated by a positive $z-$score.

Whereas,

A value below the mean is indicated by a negative $z-$score.

Calculate the $z-$ score:$z=\frac{x−\overline{x}}{SD}$

Substitute the values:

$1.82=\frac{x−51,742.44}{8210.64}$

Multiply both sides by $8210.64$:

$14,943.36=x−51,742.44$

Add $51,742.44$ to both sides:

$14,943.36+51,742.44=x−51,742.44+51,742.44$

That becomes

$x=66,685.80$

Therefore,

For New Jersey, the median household income is approx. $\$66,685.80$