Question

Suppose that the distribution of times between seismic events in an area is not symmetric. According to Chebyshev's Theorem, at least what approximate percentage of these times are within k=4.2 standard deviations of the mean? Round your answer to the nearest whole number (percent).

Answer 1

Chebyshev's Theorem suggests that approximately 94% of the times between seismic events fall within 4.2 standard deviations of the mean, after rounding to the nearest whole number.

Step-by-step explanation:

According to Chebyshev's Theorem, the inequality 1 - \(1/k^2\), where k is the number of standard deviations from the mean, can be used to determine the minimum proportion of observations that fall within k standard deviations of the mean. For k = 4.2, we first calculate k^2 which is 4.2^2 = 17.64. Then, applying Chebyshev's inequality, we get:

1 - \(1/17.64\) = 1 - 0.0567 = 0.9433 or 94.33%

Rounded to the nearest whole number, this gives us 94% as the approximate percentage of times between seismic events that are within 4.2 standard deviations of the mean.