Let X be a random variable with a normal distribution such that E(X) = µ and Var(X) = σ^2 .?

　
Use z-score chart:
http://www.regentsprep.org/Regents/math/algtrig/ATS7/ZChart.htm

P((X−µ)²/σ² < 2.706)
= P(z² < 2.706)
= P(−1.64 < z < 1.64)
= 0.9495 − 0.0505
= 0.899

------------------------------

P(X > µσ|X > µ))
= P(X > µσ and X > µ) / P(X > µ)

This probability will depend on whether µ > µσ or µσ > µ

For µ > µσ, then (X > µσ and X > µ) becomes (X > µ)
= P(X > µ) / P(X > µ)
= 1

For µσ > µ, then (X > µσ and X > µ) becomes (X > µσ)
= P(X > µσ) / P(X > µ)
= P(X > µσ) / (1/2)
= 2P(X > µσ)

------------------------------

P(µ − σ < X < µ + 2σ)
= P(−1 < z < 2)
= 0.9772 − 0.1587
= 0.8185