Question

From a sample with nequals32​, the mean duration of a​ geyser's eruptions is 3.42 minutes and the standard deviation is 1.09 minutes. Using​ Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.24 and 5.6 minutes?

Answer 1

Answer:]

At least 75% of the eruptions lasted between 1.24 and 5.6 minutes.

Explanation:

We are given the following information in the question:

n = 32

Mean = 3.42

According to Chebyshev's rule:

At least
`\bigg( 1 - \displaystyle(1)/(k^2)\bigg)`, percent of data lies within
`(\bar{x} \pm ks)`, where s is the standadrd deviation of the data and
`\bar{x}` is the mean of data.

For k = 2, we have

`1 - \displaystyle(1)/(4) = \displaystyle(3)/(4) = 75\%`

75% of data lies within the range of

`(3.42 \pm 2* 1.09)\\= (3.42 - 2.18, 3.42 + 2.18)\\= (1.24,5.6)`

Thus, at least 75% of the eruptions lasted between 1.24 and 5.6 minutes.