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From a sample n=36, the mean duration of a geysers eruption is 3.76 minutes and the standard deviation is 1.21 minutes using chebychevs theorem. Determine at least how many of the eruptions lasted between 0.13 and 7.39 minutes

Answer :

LammettHash
[tex]\mathbb P(0.13<X<7.39)=\mathbb P\left(-3<\dfrac{X-3.76}{1.21}<3\right)=\mathbb P\left(|X-\mu|<3\sigma)[/tex]

where [tex]\mu[/tex] is the mean duration and [tex]\sigma[/tex] is the standard deviation. By Chebychev's theorem, this probability is bounded below by

[tex]\mathbb P(|X-\mu|<3\sigma)\ge1-\dfrac1{3^2}=\dfrac89[/tex]

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