Question

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 1

`\mathbb P(0.13<X<7.39)=\mathbb P\left(-3<(X-3.76)/(1.21)<3\right)=\mathbb P\left(|X-\mu|<3\sigma)`

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


`\mathbb P(|X-\mu|<3\sigma)\ge1-\frac1{3^2}=\frac89`