Question

Where are the old folks? Based on data from the 2010 U.S. Census, the percent of residents aged 65 or older in the 50 states and the District of Columbia has a mean of 13.26% and standard deviation of 1.67%.

SHOW YOUR WORK!
a. Find and interpret the standardized score (z-score) for the state of Colorado, which had 9.7% of its residents aged 65 or older.
A. -3.16, indicating that Colorado has fewer older residents than the mean.
B. 1.99, indicating that Colorado has more older residents than the mean.
C. 0.93, indicating that Colorado has an average number of older residents.
D. -0.93, indicating that Colorado has an average number of older residents.

Answer 1

The standardized score (z-score) for the state of Colorado is -2.13, which indicates that Colorado has significantly fewer residents aged 65 or older compared to the national average.

Step-by-step explanation:

To find the standardized score (z-score) for the state of Colorado, where 9.7% of its residents are aged 65 or older, we use the formula:

Z = (X - μ) / σ

Where:

• X is the value to standardize (Colorado's percentage), which is 9.7%.
• μ is the mean of the population, which is 13.26%.
• σ is the standard deviation, which is 1.67%.

Plugging in the numbers:

Z = (9.7 - 13.26) / 1.67 = -3.56 / 1.67

Z = -2.13

So, the z-score for the state of Colorado is -2.13. This indicates that Colorado has significantly fewer older residents compared to the national mean (since the z-score is negative and more than 2 standard deviations below the mean).

Therefore, the correct answer is not listed among the options provided, but the closest one would be A (though the value there is not exact).