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Answer :
a. 95% of the rates between 101 and 765 per 100,000 people.
b. 68% of the rates between 267 and 599 per 100,000 people.
Based on the information provided and using the Empirical Rule for a bell-shaped distribution:
a) Approximately 95% of the rates would be between 107 and 758.
The Empirical Rule, also known as the 68-95-99.7 rule, states that in a normal distribution:
Approximately 68% of the data falls within 1 standard deviation of the mean.
Approximately 95% of the data falls within 2 standard deviations of the mean.
Approximately 99.7% of the data falls within 3 standard deviations of the mean.
In this case, the mean (μ) is 433 and the standard deviation (σ) is 166. To find the range for 95% of the rates:
Lower bound: μ - 2σ = 433 - (2 * 166) = 101
Upper bound: μ + 2σ = 433 + (2 * 166) = 765
b) Approximately 68% of the rates would be between 267 and 599.
Similarly, for 68% of the rates:
Lower bound: μ - σ = 433 - 166 = 267
Upper bound: μ + σ = 433 + 166 = 599
Therefore, you can expect to find:
95% of the rates between 101 and 765 per 100,000 people.
68% of the rates between 267 and 599 per 100,000 people.
Complete question:
In 2012, the mean rate of violent crime (per 100,000 people) in the metropolitan areas of a country was 433. The standard deviation was 166. Assume that the distribution of violent crime rates is approximately bell-shaped.
a. Using the Empirical Rule, between what two values would you expect to find about 95% of the rates? Approximately 95% of the observations fall within the interval . (Type whole numbers.)
b. Using the Empirical Rule, between what two values would you expect to find about 68% of the rates?
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