Question

From a sample with n=36, the mean duration of a​ geyser's eruptions is 3.26 minutes and the standard deviation is 0.73 minutes. Using​ Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.07 and 5.45 minutes.

Answer 1

Given that, mean = 3.26 minutes and

standard deviation = 0.73 minutes

Sample size (n) = 36

According to Chebyshev's theorem,

At least (1 - 1/k^{​​​​​​2}​​​​​) * 100% of the data fall within k standard deviations of the mean.

For k = 3

mean - 3sd = 3.26 - (3 * 0.73) = 1.07 and

mean + 3sd = 3.26 + (3 * 0.73) = 5.45

And

[ 1 - (1/3²) ] * 100 = 0.8889 * 100 = 88.89%

Therefore, at least 88.89% of the eruptions lasted between 1.07 and 5.45 minutes.

Hence, the number of the eruptions lasted between 1.07 and 5.45 minutes are, 36 * 0.8889 = 32.0004 ≈ 32

Answer : 32