A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: $$\begin{array} { l l l l l l l l l l l l l }
68 & 73 & 66 & 76 & 86 & 74 & 61 & 89 & 65 & 90 & 69 & 92 & 76 \
62 & 81 & 63 & 68 & 81 & 70 & 73 & 60 & 87 & 75 & 64 & 82 &
\end{array}$$ Suppose the mean and standard deviation are 74.04 and 9.75, respectively. If we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old?
A) approximately 81.5%
B) approximately 68%
C) approximately 95%
D) approximately 84%

Question

A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: $$\begin{array} { l l l l l l l l l l l l l } 
68 & 73 & 66 & 76 & 86 & 74 & 61 & 89 & 65 & 90 & 69 & 92 & 76 \
62 & 81 & 63 & 68 & 81 & 70 & 73 & 60 & 87 & 75 & 64 & 82 &
\end{array}$$ Suppose the mean and standard deviation are 74.04 and 9.75, respectively. If we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old?
A) approximately 81.5%
B) approximately 68%
C) approximately 95%
D) approximately 84%

Quizplus · Accepted Answer

The empirical rule states that for a mound-shaped and symmetric distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean. In this case, the mean is 74.04 and the standard deviation is 9.75. Therefore, approximately 68% of the respondents will be between 64.29 (74.04 - 9.75) and 83.79 (74.04 + 9.75) years old, and approximately 95% of the respondents will be between 54.54 (74.04 - 2 * 9.75) and 93.54 (74.04 + 2 * 9.75) years old.

A Sociologist Recently Conducted a Survey of Citizens Over 60