Introduction to Probability · Problem 8.2.6

Central Limit Theorem — Grinstead & Snell

Mathematics — Probability · law-of-large-numbers-continuous

Problem

X

is normally distributed, with mean

\mu

and variance

\sigma^2

, find an upper bound for the following probabilities, using Chebyshev's Inequality. (a)

P(|X - \mu| \geq \sigma)

. (b)

P(|X - \mu| \geq 2\sigma)

. (c)

P(|X - \mu| \geq 3\sigma)

. (d)

P(|X - \mu| \geq 4\sigma)

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