Question

From a sample with n equals 36​, the mean duration of a​ geyser's eruptions is 3.41 minutes and the standard deviation is 0.98 minutes. Using​ Chebychev's Theorem, determine at least how many of the eruptions lasted between 0.47 and 6.35 minutes.

Answer 1

Given that, mean = 3.41 minutes and

standard deviation = 0.98 minutes

sample size (n) = 36

According to Chebyshev's theorem, at least (1 - 1/k​​​​​​2​​​) of the data fall within k standard deviations of the mean.

For k = 3

mean - 3sd = 3.41 - (3 * 0.98) = 0.47 and

mean + 3sd = 3.41 + (3 * 0.98) = 6.35

And

At least (1 - 1/32) = 0.8889, of the eruptions lasted between 0.47 and 6.35 minutes.

Here, 36 * 0.8889 ≈ 32

Therefore, at least 32 of the eruptions lasted between 0.47 and 6.35 minutes.