Question

Using Chebyshev's inequality,

Which of the following is the correct output for Chebyshev(180.,0.3,1.1) O 0.999 o 0.924 o 0.976X O 2.333

Answer 1

ans) .999 here k=100, mean = .3 and s.d. = 1.1

According to Chebyshev's rule, the probability that X is within k standard deviations of the mean can be estimated as follows:

\Pr(|X - \mu| < k \sigma) \le 1 - \frac{1}{k^2}Pr(∣X−μ∣<kσ)≤1−k21​

In this case, since k = 100, the probability that XX is within 100 standard deviations of the mean is at least:

\Pr(|X - \mu| < k \sigma) \le 1 - \frac{1}{ 100^2} = 0.9999Pr(∣X−μ∣<kσ)≤1−10021​=0.9999