Math Problem Statement
Yearly rainfall amounts (in millimeters) of a city are in the table.
Yearly Rainfall Amounts
113.9 61.9 97.9 72.6 186.2 231.5 210.5 207.6 247.4 177.4 221.8 95.6 89.0 167.9 74.5 88.8 43.3 47.6 144.4 115.7 90.0 140.8 100.5 28.7 43.7 180.7 43.0 145.8 100.4 121.4 71.8 6.5 150.5 219.4 194.4 105.6 133.5 174.8 184.9 150.3 100.5 43.3 200.1 226.0 46.7 160.8 136.1
Using technology, find the mean and standard deviation. Round to the nearest hundredth, if necessary. The mean of the data is mm.
The standard deviation of the data is mm.
Use Chebyshev’s theorem to find an interval centered about the mean yearly rainfalls in which you would expect at least 75% of the yearly rainfalls to fall.
At least 75% of the yearly rainfalls will fall between mm and mm.
Use Chebyshev’s theorem to find an interval centered about the mean yearly rainfalls in which you would expect at least 88.9% of the yearly rainfalls to fall.
At least 88.9% of the yearly rainfalls will fall between mm and mm.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Standard Deviation
Chebyshev's Theorem
Formulas
Mean formula: (sum of values) / (number of values)
Standard deviation formula: sqrt((Σ(xi - μ)^2) / N)
Chebyshev's Theorem: (1 - (1/k^2)) * 100%
Theorems
Chebyshev's Theorem
Suitable Grade Level
Grades 10-12
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