Question

Foreign-born residents The percentile plot below shows the distribution of the percent of foreign-born residents in the $50$ states.

(a) The highlighted point is for Maryland. Describe what the graph tells you about this state.

(b) Use the graph to estimate the ${30}^{th}$ percentile of the distribution. Explain your method.

Short answer

Part(a) It is observed that Maryland has about $13\%$, foreign-born residents.

Part(b) The 30% percentile is approximately $4.5\%$ foreign-born residents in the $50$ states.

Step-by-step solution

Part (a) Step 1. Given

Part (a) Step 2. Concept

A score in the ${95}^{th}$ percentile is a figure on a scale of $100$ that represents the percent of a distribution that is equal to or below it.

Part (a) Step 3. Explanation

$70$Its purpose is to describe the highlighted point in the percentile graph provided.

Procedure

Step 1: Draw a horizontal line from the vertical axis' highlighted point.

Step 2: From this point, draw a vertical line to the horizontal axis.

Step 3: The line intersects the vertical axis at about$70$ degrees and the horizontal axis at about 13 degrees.

The aforesaid technique is depicted in the graph below.

According to the graph above, Maryland has a foreign-born population of around $13\%$

Therefore, Maryland has about $13\%$ foreign-born residents.

Part (b) Step 1. Explanation

It's supposed to calculate the distribution's ${30}^{th}$ percentile.

Procedure

Step1: Determine the place on the ogive where the line intersects the ogive by drawing a horizontal line from the value $30$ on the vertical axis.

Step 2: From this point, draw a vertical line to the horizontal axis.

Step 3: At about $4.5$, the line intersects the axis.

The technique is depicted in the graph below:

Therefore, the ${30}^{th}$percentile is approximately $4.5\%$of foreign-born residents in the $50$ states.