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Chapter 2: Q 91. (page 144)

Making money (2.1) The parallel dot plots show the total family income of randomly chosen individuals from Indiana (38 individuals) and New Jersey (44 individuals). Means and standard deviations are given below the dot plots.

Consider individuals in each state with total family incomes of $95,000 Which individual has a higher income, relative to others in his or her state? Use percentiles and z-scores to support your answer.

Short Answer

Expert verified

In comparison to others in his or her state, an Indiana resident enjoys a better income.

Step by step solution

01

Given information

02

Concept

The formula used:z=x−μσ

03

Calculation

For Indiana:

Calculate the z−score:

z=x−μσ=95,000−47,40029,400=47,60029,400≈1.62

For New Jersey:

Calculate the z−score:

z=x−μσ=95,000−58,10041,900=36,90041,900≈0.88

Compare the z−scores:

When z scores are compared, it shows that a person with a higher z−score has a greater income than others in his or her state.

As a result, an Indiana resident has a higher income than others in his or her state.

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Most popular questions from this chapter

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A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68–95–99.7 rule.

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(c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)

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