Question

From a sample with n =36, the mean duration of geyser’s eruption is 3.11 minutes and the standard deviations is 0.55 minutes. Using chebychev’s theorem, determine at least how kany of the eruptions lasted between 1.46 and 4.76 minutes. Atleast - of reuptions lasted between 1.46 and 4.76 minutes

Answer 1

sample size,n=36

mean=3.11 minutes

std dev=0.55 minutes

now 1.46=mean-3*std dev

4.76=mean+3*std dev

Now by Chebyshev's theorem,

For any numerical data set,

• at least 3/43/4 of the data lie within two standard deviations of the mean, that is, in the interval with endpoints x¯±2sx¯±2s for samples and with endpoints μ±2σμ±2σ for populations;
• at least 8/9 of the data lie within three standard deviations of the mean, that is, in the interval with endpoints ±3s for samples and with endpoints μ±3σ for populations;
• at least 1−1/k^2 of the data lie within kk standard deviations of the mean, that is, in the interval with endpoints ±ks for samples and with endpoints μ±kσ for populations, where kk is any positive whole number that is greater than 11.

Thus, by chebyshevs theorem, atleast 36*(8/9) =32 eruptions lasted between 1.46 and 4.76 minutes(Answer)