The table shows the inflation-adjusted annual income per person in 1990 and 2011 for each listed country. Which country had the smallest relative increase in annual income per person from 1990 to 2011? What was the smallest relative increase? |1990 2011 |Country A $33,304 $41,451 Country B $23,036 $30,829 Country C $1,986 $7,656 Country D $893 $1,140 Country had the smallest relative increase in annual income per person from 1990 to 2011. It was about %. (Round to the nearest tenth as needed.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Income Growth Analysis: 1990 to 2011
The table below displays the inflation-adjusted annual income per person in 1990 and 2011 for four different countries.
| | 1990 | 2011 |
|------------|--------|--------|
| Country A | $33,304| $41,451|
| Country B | $23,036| $30,829|
| Country C | $1,986 | $7,656 |
| Country D | $893 | $1,140 |
#### Question:
Which country had the smallest relative increase in annual income per person from 1990 to 2011? What was the smallest relative increase percentage?
**Solution:**
1. To find the smallest relative increase, calculate the percentage increase for each country using the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Income in 2011} - \text{Income in 1990}}{\text{Income in 1990}} \right) \times 100 \]
2. Calculate the percentage increase for each country:
- **Country A**:
\[
\left( \frac{41451 - 33304}{33304} \right) \times 100 \approx 24.4\%
\]
- **Country B**:
\[
\left( \frac{30829 - 23036}{23036} \right) \times 100 \approx 33.9\%
\]
- **Country C**:
\[
\left( \frac{7656 - 1986}{1986} \right) \times 100 \approx 285.5\%
\]
- **Country D**:
\[
\left( \frac{1140 - 893}{893} \right) \times 100 \approx 27.6\%
\]
Hence, **Country A** had the smallest relative increase in annual income per person from 1990 to 2011, with an increase of approximately **24.4%**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b01cae-a992-40a5-9370-7280dcc318cb%2F2b6b1654-7cd6-42d7-93a2-d254c5e39943%2Fr35rjhj.png&w=3840&q=75)
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