Chebyshev’s inequality (Section 2.4) 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 ȼ N(μ, σ²). Compute P(|X − μ; μ| ≥...

Chebyshev’s inequality (Section 2.4) 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 ȼ N(μ, σ²). Compute P(|X − μ; 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?