Kira keeps track of how much time she spends walking her dog each morning. Her data
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M∠X = 54.3°.
Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X
Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X
Chebyshev's theorem in statistics states that for many probability distributions, no more than 1/k² of measured values will be k standard deviations away from the mean.
Because the area under the probability distribution curve is equal to 1, Chebyshev's theorem means that the shaded area shown in the figure is equal to 1 - 1/k².
When k = 1.75, the shaded area is
1 - 1/1.75² = 0.7635 = 67.35%
Therefore the percent of the area within +/- 1.75 standard deviations from the mean is
67.35/2 = 33.7%, which is at least 33% of the observations.
Answer:
According to the Chebyshev theorem, at least 33% of the observations lie within +/- standard deviations from the mean.
Because the area under the probability distribution curve is equal to 1, Chebyshev's theorem means that the shaded area shown in the figure is equal to 1 - 1/k².
When k = 1.75, the shaded area is
1 - 1/1.75² = 0.7635 = 67.35%
Therefore the percent of the area within +/- 1.75 standard deviations from the mean is
67.35/2 = 33.7%, which is at least 33% of the observations.
Answer:
According to the Chebyshev theorem, at least 33% of the observations lie within +/- standard deviations from the mean.