Chapter 2.2, Problem 91E

To determine

Individual with higher income, relative to others in his or her state.

Answer to Problem 91E

Individual from Indiana has a higher income, relative to others in his or her state.

Explanation of Solution

Given information:

For Indiana:

Value, $x=\$95,000$

Mean, $\mu =\$47,400$

Standard deviation, $\sigma =\$29,400$

For New Jersey:

Value, $x=\$95,000$

Mean, $\mu =\$58,100$

Standard deviation, $\sigma =\$41,900$

For Indiana:

Calculate the z − score:

  $z=\frac{x-\mu }{\sigma }=\frac{95,000-47,400}{29,400}=\frac{47,600}{29,400}\approx 1.62$

For New Jersey:

Calculate the z − score:

  $z=\frac{x-\mu }{\sigma }=\frac{95,000-58,100}{41,900}=\frac{36,900}{41,900}\approx 0.88$

Compare the z − scores:

The comparison of z − scores depicts that individual with higher z − score has a higher income, relative to others in his or her state.

Thus,

Individual from Indiana has a higher income, relative to others in his or her state.