Chapter 2.1, Problem 2E

(a)

To determine

To find: the percentile for Colorado

Answer to Problem 2E

There are $8\%$ of the states having residents aged 65 and older below $10.1\%$

Explanation of Solution

Given:

  $10.1\%$ of the residents of Colorado aged 65 or older.

  $\begin{array}{cc}7& 0\\ 8& 8\\ 9& 8\\ 10& 019\\ 11& 16777\\ 12& 01122456778999\\ 13& 0001223344455689\\ 14& 023568\\ 15& 24\\ 16& 9\\ \begin{array}{l}\text{ Key }=1512\text{ means }15.2\%\text{ of }\hfill \\ \text{thisstat<msup><mo>e</mo><mo>′</mo></msup> sresidentsare65}\hfill \\ \text{ or older }\hfill \end{array}& \\ & \end{array}$

Calculation:

From the stem plot, we can see that only 4 of the 50 states $(7.0\%,8.8\%,9.8\%\text{ and }10.0\%)$ having residents aged 65 and older below $10.1\%$

Percentile for Colorado computed as follows:

  $\frac{4}{50}=0.08=8\%$

So, Colorado with residents aged 65 and order below

  $10.1\%$ is at the $8^{\text{th }}$ percentile. In other words, there are $8\%$ of the states having residents aged 65 and older below $10.1\%$

Conclusion:

Therefore, there are $8\%$ of the states having residents aged 65 and older below $10.1\%$

(b)

To determine

To find: the percentile for Rhode Island

Answer to Problem 2E

  $80\%$ of the states having residents aged 65 and older below $13.9\%$

Explanation of Solution

Given:

  $13.9\%$ of theresidents of Rhode Island aged 65 or older.

  $\begin{array}{cc}7& 0\\ 8& 8\\ 9& 8\\ 10& 019\\ 11& 16777\\ 12& 01122456778999\\ 13& 0001223344455689\\ 14& 023568\\ 15& 24\\ 16& 9\\ \begin{array}{l}\text{ Key }=1512\text{ means }15.2\%\text{ of }\hfill \\ \text{thisstat<msup><mo>e</mo><mo>′</mo></msup> sresidentsare65}\hfill \\ \text{ or older }\hfill \end{array}& \\ & \end{array}$

Calculation:

From the stem plot, we can see that 40 of the 50 states having residents aged 65 and olderbelow $13.9\%$

Percentile for Rhode Island computed as follows:

  $\frac{40}{50}=0.80=80\%$

So, Rhode Island with residents aged 65 and older below $13.9\%$ is at the ${80}^{\text{th }}$ percentile. Inother words, $80\%$ of the states having residents aged 65 and older below $13.9\%$

Conclusion:

Therefore, $80\%$ of the states having residents aged 65 and older below $13.9\%$

(c)

To determine

To find:whether Colorado or Rhode Island is unusual.

Answer to Problem 2E

Colorado is the more unusual state

Explanation of Solution

Calculation:

Colorado is the more unusual state having only $8\%$ of the states with smaller percentages of theresidents aged 65 and older. Rhode Island has a value that is closer to the center of the distribution with $80\%$ lower and $20\%$ as larger or larger

Conclusion:

Therefore, Colorado is the more unusual state