Question

From a sample with n=36, the mean duration of a geyser's eruptions is 3.62 minutes and the standard deviation is 0.67 minutes. Using chebychev's theorem, determine at least how many of the eruptions lasted between 2.28 and 4.96 minutes.

At least__ of the eruptions lasted between 2.28 and 4.96 minutes.

Answer 1

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Answer:

2.28 and 4.96 are 2 standard deviations from the mean of 3.62 (3.62 +- 2*0.67)

=>

Now using Chebyshev's rule with k=2, we know that at least:

Therefore, at least 75% of data is within 2 standard deviations from the mean.

Now the number of eruptions between 2.28 minutes and 4.96 minutes is:

75% * 36 = 27 samples