Chapter 2.1, Problem 10E

(a)

To determine

Whether North Dakota is an unusually wealthy state.

Answer to Problem 10E

North Dakota is not an unusually wealthy state.

Explanation of Solution

Given information:

  

Calculations:

First

Draw the vertical line intersecting the horizontal axis at 56, because $55,766 is approx. fifty six thousand dollars.

Then

Draw the horizontal line through the intersection of curve and vertical line.

Note that

Horizontal line roughly intersecting the vertical axis at 68.4.

That implies

Around 68.4% of the states have lower median household income.

And

The rest 31.6% of the states have higher median household income.

Since

The percentage less than 5% is considered to be small.

Thus,

North Dakota is not usually wealthy, because 31.6% cannot be considered as small.

  

(b)

To determine

Interpretation of 90^th percentile of the distribution.

Answer to Problem 10E

The median household income of 90% of all the states is less than $64,000.

Explanation of Solution

Given information:

  

Calculations:

The data value represented by the x^th percentile has x% of the data values below it.

That implies

The data value represented by the 90^th percentile has 90% of the data values below it.

Now,

Draw the horizontal line intersecting the vertical axis at 90.

Then

Draw the vertical line through the intersection of curve and horizontal line.

Note that

Vertical line roughly intersecting the horizontal axis at 64.

That implies

The 90^th percentile is roughly at $64,000.

Thus,

The median household income of 90% of all the states is less than $64,000.