#chebyshev-inequality

Question 1: Single choice

Someone says: "My random variable has mean 1 and standard deviation 2, and 25% of my samples were larger than 9." Should you believe them?

No: 9 is 4 standard deviations above the mean, and Chebyshev allows at most $1/16 = 6.25\%$ that far out1
Yes: Chebyshev bounds 4-standard-deviation events by $1/4 = 25\%$ , so the claim sits exactly at the limit2
Yes: Chebyshev's inequality only holds for Gaussians, so any tail is possible for this variable3
No: a Gaussian puts only 0.003% beyond 4 standard deviations, the most any distribution can4