If [math]X[/math] is normally distributed, with mean [math]\mu[/math] and variance [math]\sigma^2[/math], find an upper bound for the following probabilities, using Chebyshev's Inequality.

• [math]P(|X - \mu| \geq \sigma)[/math].
• [math]P(|X - \mu| \geq 2\sigma)[/math].
• [math]P(|X - \mu| \geq 3\sigma)[/math].
• [math]P(|X - \mu| \geq 4\sigma)[/math].

Now find the exact value using the program NormalArea or the normal table in Appendix A, and compare.