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Answer :
Final answer:
In 2011, the mean rate of violent crime for the northeastern states was 314 per 100,000 people, with a standard deviation of 118. The expected range for about 95% of the rates is approximately 78 to 550, while the range for about 68% of the rates is approximately 196 to 432. A violent crime rate of 896 would be considered unusual as it falls outside these ranges.
Explanation:
The mean rate of violent crime for the 10 northeastern states in 2011 was 314 per 100,000 people, with a standard deviation of 118. Assuming a bell-shaped and symmetric distribution, we can use the Empirical Rule to estimate the range of values where we would expect to find a certain percentage of rates.
a. To find the range where we would expect to find about 95% of the rates, we can go two standard deviations above and below the mean. In this case, that would be 314 - 2(118) to 314 + 2(118), which gives a range of approximately 78 to 550.
b. To find the range where we would expect to find about 68% of the rates, we can go one standard deviation above and below the mean. In this case, that would be 314 - 118 to 314 + 118, which gives a range of approximately 196 to 432.
c. A violent crime rate of 896 would be considered unusual because it falls outside the range of values expected based on the mean and standard deviation. It is more than three standard deviations above the mean, so it would be considered an outlier.
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