Answer:]
At least 75% of the eruptions lasted between 1.24 and 5.6 minutes.
Step-by-step explanation:
We are given the following information in the question:
n = 32
Mean = 3.42
According to Chebyshev's rule:
At least [tex]\bigg( 1 - \displaystyle\frac{1}{k^2}\bigg)[/tex], percent of data lies within [tex](\bar{x} \pm ks)[/tex], where s is the standadrd deviation of the data and [tex]\bar{x}[/tex] is the mean of data.
For k = 2, we have
[tex]1 - \displaystyle\frac{1}{4} = \displaystyle\frac{3}{4} = 75\%[/tex]
75% of data lies within the range of
[tex](3.42 \pm 2\times 1.09)\\= (3.42 - 2.18, 3.42 + 2.18)\\= (1.24,5.6)[/tex]
Thus, at least 75% of the eruptions lasted between 1.24 and 5.6 minutes.
