Chebyshevs inequality states that for any random variable X with mean and variance 2 , and for any positive number k, P(|X

Chebyshev’s inequality states that for any random variable X with mean μ and variance σ², and for any positive number k, P(|X − μ| ≥ kσ) ≤ 1/k². Let X ∼ N(μ, σ²). Compute P(|X −μ| ≥ kσ) for the values k = 1, 2, and 3. Are the actual probabilities close to the Chebyshev bound of 1/k², or are they much smaller?