Let X be a normal random variable with mean zero and variance 9. If a = P(X ≥ 3) then P(|X| ≤ 3) equals: 

The correct answer is option 1

Data:

mean = μ = 0;

variance = σ² = 9 

P(X ≥ 3) = a

Calculation:

Standard deviation = σ = √variance  = √9  = 3

P(|X| ≤ 3)  = P(-3 ≤ X ≤ 3)

P(-∞ ≤ X ≤ +∞ ) = P(X ≤ 3) + P(-3 ≤  X ≤ 3) + P(X ≥ 3) = 1

Since it is a normal distribution with z = 1

P(X ≥ 3) = P(X ≤ 3) = a

 P(X ≤ 3) + P(-3 ≤  X ≤ 3) + P(X ≥ 3) = 1

a + P(|X| ≤ 3) + a = 1

∴ P(|X| ≤ 3) = 1 - 2a