SOLUTION: Use Chebyshev’s theorem to find what percent of the values will fall between 59 and 107 for a data set with mean of 83 and standard deviation of 8. - Use the Empirical Rule to fi

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Question 308487: Use Chebyshev’s theorem to find what percent of the values will fall between 59 and 107 for a data set with mean of 83 and standard deviation of 8.
- Use the Empirical Rule to find what two values 67% of the data will fall between for a data set with mean 103 and standard deviation of 12.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use Chebyshev’s theorem to find what percent of the values will fall between
59 and 107 for a data set with mean of 83 and standard deviation of 8.
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(59-83)/8 = -3
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(107-83)/8 = 3
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% of population within 3 std of mean = 1-(1/3)^2 = 8/9 = 88.89%
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- Use the Empirical Rule to find what two values 67% of the data will fall between for a data set with mean 103 and standard deviation of 12.
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1st: Draw a normal curve and sketch 67% of the population around
a mean of 103.
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Amount of population to the left and to the right of 103 is 0.67/2 = 0.3350
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The % of population in a left tail of 0.50-0.3350 = 0.1650
The associated z-value = invNorm(0.1650) = -0.9741
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Using x = zs + u
x = -0.9741*12+103 = 91.31
x = +0.9741*12+103 = 114.69
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67% of the population will be between those two x-values.
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Cheers,
Stan H.
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