Math Help Please?

Since we are working with the exponential distribution, we have μ = σ = 1/λ.

So, P(|X − μ| ≥ 3σ)
= P(|X − 1/λ| ≥ 3/λ)
= P(X − 1/λ ≤ -3/λ or X − 1/λ ≥ 3/λ)
= P(X ≤ -2/λ or X ≥ 4/λ)
= P(X ≥ 4/λ), since X ≥ 0 for the exponential distribution
= ∫(x = 4/λ to ∞) λe^(-λx) dx, using the pdf of the exponential distribution
= -e^(-λx) {for x = 4/λ to ∞}
= 0 - (-e^(-4))
= e^(-4).

I hope this helps!

I answered your previous question about *one* standard deviation. This is the exact same question, but with *three* standard deviations, and also being *outside* the range rather than inside. Using the same rule, the answer is:
100% - 99.7%
≈ 0.3%.

P(|X − μ| < 3σ) = 99.7%
hence
P(|X − μ| ≥ 3σ) = ...